Cladding layer thickness prediction model construction method and device for double-metal composite pipeline, and cladding layer thickness prediction method and device

CN122242173BActive Publication Date: 2026-09-08XINJIANG PETROLEUM ENG DESIGN CO LTD +2
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Patent Information

Application Number
CN202610686286.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2026-05-19
Publication Date
2026-09-08
Estimated Expiration
2046-05-19

AI Technical Summary

Technical Problem

[0006]本发明提供了一种用于双金属复合管道的堆焊层厚度预测模型构建方法、装置及堆焊层厚度预测方法、装置,克服了上述现有技术之不足,其能有效解决现有技术不能明确堆焊层厚度与渗入母材的等效充氢压力之间的映射关系,进而不能预测最优堆焊层厚度的问题

Benefits of technology

[0017]本发明采用模拟与试验相结合的方式,利用氢渗透试验获取不同堆焊层厚度的双金属复合管道对应试样各区域的氢渗透参数,针对不同堆焊层厚度的双金属复合管道,建立对应的双金属复合管道三维有限元计算模型,模拟堆焊过程,先后顺序耦合计算堆焊过程的温度场、应力场和氢扩散场建立堆焊层厚度与等效充氢压力之间的定量映射关系曲线,得到堆焊层厚度预测模型,后续根据确定的能进入母材的等效充氢压力,在确保碳钢基体不发生氢脆的前提下,使用堆焊层厚度预测模型预测得到双金属复合管道的最优堆焊层厚度,由此合理控制堆焊层的材料成本,使用最经济的成本获得最大的实用性,为高压输氢复合管道的工程化设计提供理论依据。且相较于机器学习等方法,该过程简单、易操作、对计算设备要求不高,成本低,且所构建的堆焊层厚度预测模型预测准确度高,能广泛适用于双金属复合管道的堆焊层厚度预测。

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Abstract

The present application relates to a kind of double metal composite pipeline surfacing technical field, a kind of surfacing layer thickness prediction model construction method, surfacing layer thickness prediction method and related device for double metal composite pipeline, including obtaining the hydrogen permeation parameter of the sample corresponding to different surfacing layer thicknesses of double metal composite pipeline;Simulate the corresponding surfacing process of different surfacing layer thicknesses of double metal composite pipeline, obtain the hydrogen distribution nephogram of each surfacing layer thickness;Based on the hydrogen distribution nephogram of each surfacing layer thickness, the quantitative mapping relationship curve between surfacing layer thickness and equivalent hydrogen charging pressure is established, and the surfacing layer thickness prediction model is obtained.The present application adopts the way of simulation and test, constructs surfacing layer thickness prediction model, and the optimal surfacing layer thickness of double metal composite pipeline is obtained by prediction, thereby reasonably control the material cost of surfacing layer, the most reasonable cost is used to obtain the maximum practicability, and provide theoretical basis for the engineering design of high-pressure hydrogen transmission composite pipeline.
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Description

Technical Field

[0001] This invention relates to the field of overlay welding technology for bimetallic composite pipes, and to a method and apparatus for constructing a prediction model for the overlay thickness of bimetallic composite pipes, as well as a method and apparatus for predicting the overlay thickness. Background Technology

[0002] Currently, approximately 3,000 kilometers of hydrogen pipelines worldwide operate at pressures up to 10 MPa. These pipelines are typically constructed using low-strength steel with a strength not exceeding X52. While low-strength steel pipelines can be used for hydrogen transport, their pressure-bearing capacity is limited. The reason high-strength steel is not used in hydrogen pipelines is that, although it allows for reduced wall thickness and increased operating pressure, it is prone to hydrogen embrittlement. Hydrogen embrittlement occurs when hydrogen atoms diffuse into the metal, reducing the plasticity and toughness of the pipeline steel and even inducing brittle fracture. This can lead to delayed cracking of the pipeline at loads far below design limits, posing an extremely high risk. To avoid the problems associated with low-strength and high-strength steels, bimetallic composite pipes are used as hydrogen transport pipelines. The inner layer (corrosion-resistant alloy) of the bimetallic composite pipe is made of a face-centered cubic (FCC) material, such as austenitic stainless steel or nickel-based alloys. These materials have an extremely low diffusion coefficient for hydrogen atoms (several orders of magnitude lower than carbon steel), making them excellent hydrogen barriers. The outer carbon steel layer is made of high-strength steel (such as X70). High-strength steel provides mechanical strength, allowing for thinner pipe walls, reduced weight, and the ability to withstand higher pressures. During operation, the hydrogen transported in the pipeline first comes into contact with the inner layer. Because hydrogen permeates very slowly in this layer, most hydrogen atoms cannot penetrate to the outer carbon steel layer. Therefore, the outer high-strength steel layer hardly comes into contact with hydrogen, thus avoiding hydrogen embrittlement.

[0003] In research on the welding process and corrosion performance of bimetallic composite pipes, mechanical composite methods are often adopted in engineering to reduce production costs, supplemented by pipe end internal wall surfacing. This involves first surfacing a layer of high-alloy material, followed by welding with high-alloy welding materials. This process successfully solves the problem of cracking in the welded joints of mechanically composite pipes. Furthermore, the main function of the lining and surfacing layer is to block hydrogen gas, controlling the peak hydrogen concentration penetrating into the carbon steel matrix within safe limits. Therefore, changes in the surfacing layer thickness directly affect the peak hydrogen concentration penetrating the matrix. Given the high cost of high-alloy surfacing materials, it is desirable to minimize the thickness of the lining or surfacing layer while ensuring that the carbon steel matrix does not experience hydrogen embrittlement. However, current technology cannot clearly define the mapping relationship between the surfacing layer thickness and the equivalent hydrogen charging pressure penetrating the base material. Predicting the optimal surfacing layer thickness from an economic and practical perspective is crucial to guiding the welding process.

[0004] In the prior art, Chinese patent document CN116618878A discloses a method for determining pre-welding process parameters, an online prediction method for welding quality, an apparatus, and a storage medium, aiming to solve the technical problem of welding defects generated during complex welding processes. It includes: before welding, inputting the set pre-welding process parameters into a pre-built and trained welding quality prediction model; cyclically correcting the pre-welding process parameters based on the output results of the welding quality prediction model until the desired welding quality is achieved; during the welding process, collecting welding parameters; and inputting the welding parameters into the pre-built and trained welding quality prediction model to obtain the welding quality prediction result. This invention uses a pre-welding process parameter determination method to ensure parameter accuracy and an online welding quality prediction method to achieve welding quality assessment. However, this invention cannot predict the thickness of the weld overlay for bimetallic composite pipes.

[0005] In the prior art, Chinese patent document CN115730520A discloses a method and system for predicting and virtually simulating the morphology of welded seams. The method of this invention includes collecting and standardizing the process parameters of gas shielded welding; inputting the standardized process parameters into a weld morphology prediction neural network model to obtain the weld width and depth; the virtual simulation method for the morphology of welded seams of this invention includes using the geometric parameters of the weld bead and the weld width Y... w and melting depth Y d A virtual simulation model of the weld cross-sectional morphology and a virtual simulation model of the weld surface morphology are generated, based on the weld width Y. w and melting depth Y d The generated fitted curve represents the top profile curve of the weld bead, and stacked ellipses along the welding direction represent the molten pool elements. This invention enables accurate prediction of the weld morphology of gas-shielded welds, and achieves dynamic virtual simulation of the weld morphology based on the predicted weld morphology. However, this invention cannot predict the weld overlay thickness for bimetallic composite pipes. Summary of the Invention

[0006] This invention provides a method and apparatus for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, and a method and apparatus for predicting the weld overlay thickness. It overcomes the shortcomings of the prior art and can effectively solve the problem that the prior art cannot clearly define the mapping relationship between the weld overlay thickness and the equivalent hydrogen charging pressure penetrating the base material, and thus cannot predict the optimal weld overlay thickness.

[0007] One of the technical solutions of this invention is achieved through the following measures: a method for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, comprising: Hydrogen permeation parameters were obtained for each region of bimetallic composite pipe samples with different weld overlay thicknesses. The hydrogen permeation parameters included the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the weld overlay. The welding process of bimetallic composite pipes with different weld overlay thicknesses was simulated to determine the stress field generated during the welding process. For bimetallic composite pipes with different weld overlay thicknesses, the corresponding hydrogen permeation parameters and stress fields were used as initial and boundary conditions to simulate hydrogen distribution cloud maps for each weld overlay thickness. Based on the hydrogen distribution cloud map of each weld overlay thickness, the equivalent hydrogen charging pressure that can enter the base material is determined, and a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure is established to obtain a weld overlay thickness prediction model.

[0008] The following are further optimizations and / or improvements to the above-mentioned technical solution: The above-mentioned methods for obtaining hydrogen permeation parameters in various regions of bimetallic composite pipe samples with different weld overlay thicknesses include: The sample parent material was subjected to a high-pressure gas phase hydrogen permeation test under hydrogen transport pressure to obtain the hydrogen permeation curve of the sample parent material. The curve was linearly fitted to obtain the slope of the hydrogen permeation curve. The hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the parent material were calculated using steady-state permeation current density and hydrogen permeation curve slope. Electrochemical hydrogen permeation experiments were conducted on the weld overlay of the sample using a Devanathane-Stachurski dual-electrolysis cell hydrogen permeation apparatus to obtain the hydrogen permeation curve of the weld overlay. The hydrogen diffusion coefficient was calculated using the time lag method. The average hydrogen concentration in the weld overlay of the sample was obtained by pre-charging hydrogen and TDS thermal desorption mass spectrometry, and the subsurface adsorbed hydrogen concentration and hydrogen solubility were determined.

[0009] The above simulation of the welding process for bimetallic composite pipes with different weld overlay thicknesses determines the stress field generated during the welding process. For bimetallic composite pipes with different weld overlay thicknesses, the corresponding hydrogen permeation parameters and stress field are used as initial and boundary conditions to simulate hydrogen distribution cloud maps for each weld overlay thickness, including: For bimetallic composite pipes with different weld overlay thicknesses, a corresponding three-dimensional finite element calculation model for bimetallic composite pipes is established. The welding process was simulated for each three-dimensional finite element calculation model of bimetallic composite pipes to obtain the temperature field of the corresponding welding process. The temperature field of the welding process is used as a predefined field and applied to the corresponding three-dimensional finite element calculation model of the bimetallic composite pipe. The welding residual stress generated during the welding process is sequentially coupled and calculated to form the stress field of the corresponding welding process. Using the hydrogen diffusion parameters and stress field corresponding to a bimetallic composite pipe with a certain weld overlay thickness as initial and boundary conditions, the corresponding hydrogen diffusion field is calculated, and a hydrogen distribution cloud map is established. This process is repeated for all bimetallic composite pipes with different weld overlay thicknesses to establish hydrogen distribution cloud maps for each weld overlay thickness.

[0010] The above also includes checking the temperature field of all welding processes by adjusting the parameters of the double ellipsoidal heat source and the cross-sectional shape and size of the simulated weld bead.

[0011] The above-mentioned ABAQUS simulation software's birth and death element technology and DFLUX heat source subroutine were used to simulate the welding process of each bimetallic composite pipe's three-dimensional finite element calculation model.

[0012] Based on the hydrogen distribution cloud map of each weld overlay thickness, the equivalent hydrogen charging pressure that can penetrate the base material is determined, including: Based on the hydrogen distribution cloud map of the weld overlay thickness, the maximum hydrogen concentration that can enter the base material is extracted; The maximum hydrogen concentration that can enter the parent material is converted into the equivalent hydrogen charging pressure that can enter the parent material, and the conversion formula is as follows: in, P eq The equivalent hydrogen charging pressure required to enter the parent material, expressed in MPa; C max This represents the maximum hydrogen concentration within the parent material, expressed in ppm. S Hydrogen solubility in the weld overlay, in ppm atm -1 / 2 .

[0013] The above-mentioned specimens are homogeneous circular specimens for processing the weld overlay and the base material, with a specimen diameter of 24 mm and a specimen thickness of 2 mm.

[0014] The second technical solution of the present invention is achieved through the following measures: a method for predicting the thickness of the weld overlay in bimetallic composite pipes, comprising: Obtain the equivalent hydrogen charging pressure that can enter the parent material in the bimetallic composite pipe to be predicted; The equivalent hydrogen charging pressure that can enter the base material is input into the weld overlay thickness prediction model to obtain the weld overlay thickness of the bimetallic composite pipe to be predicted. The weld overlay thickness prediction model is constructed using the weld overlay thickness prediction model construction method for bimetallic composite pipes.

[0015] The third technical solution of the present invention is achieved through the following measures: a device for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, comprising: The hydrogen permeation parameter acquisition unit acquires the hydrogen permeation parameters of each region of the bimetallic composite pipe sample with different weld overlay thicknesses. The hydrogen permeation parameters include the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the weld overlay. The hydrogen distribution cloud map drawing unit simulates the welding process of bimetallic composite pipes with different weld overlay thicknesses, determines the stress field generated during the welding process, and uses the corresponding hydrogen permeation parameters and stress field as initial and boundary conditions for bimetallic composite pipes with different weld overlay thicknesses to simulate and obtain hydrogen distribution cloud maps for each weld overlay thickness. The model building unit determines the equivalent hydrogen charging pressure that can enter the base material based on the hydrogen distribution cloud map of each weld overlay thickness, establishes a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure, and obtains a weld overlay thickness prediction model.

[0016] The fourth technical solution of the present invention is achieved through the following measures: a device for predicting the thickness of the weld overlay in bimetallic composite pipes, comprising: The prediction data acquisition unit acquires the equivalent hydrogen charging pressure that can enter the parent material in the bimetallic composite pipe to be predicted. The prediction unit takes the equivalent hydrogen charging pressure that can enter the base material as input to the weld overlay thickness prediction model to obtain the weld overlay thickness of the bimetallic composite pipe to be predicted. The weld overlay thickness prediction model is constructed using the weld overlay thickness prediction model construction method for bimetallic composite pipes.

[0017] This invention employs a combination of simulation and experimentation. Hydrogen permeation tests are used to obtain hydrogen permeation parameters for different regions of bimetallic composite pipe samples with varying weld overlay thicknesses. For each bimetallic composite pipe with a different weld overlay thickness, a corresponding three-dimensional finite element model is established to simulate the welding process. The temperature, stress, and hydrogen diffusion fields of the welding process are sequentially coupled and calculated to establish a quantitative mapping curve between the weld overlay thickness and the equivalent hydrogen charging pressure, resulting in a weld overlay thickness prediction model. Subsequently, based on the determined equivalent hydrogen charging pressure that can penetrate the base material, and ensuring that the carbon steel matrix does not experience hydrogen embrittlement, the optimal weld overlay thickness for the bimetallic composite pipe is predicted using this model. This allows for reasonable control of the weld overlay material cost, achieving maximum practicality at the most economical cost, and providing a theoretical basis for the engineering design of high-pressure hydrogen transport composite pipes. Compared to methods such as machine learning, this process is simple, easy to operate, requires less sophisticated computing equipment, and is low-cost. Furthermore, the constructed weld overlay thickness prediction model has high prediction accuracy and can be widely applied to the prediction of weld overlay thickness in bimetallic composite pipes. Attached Figure Description

[0018] Appendix Figure 1This is a schematic diagram of the process for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, as provided in an embodiment of the present invention.

[0019] Appendix Figure 2 This is a schematic diagram of the method for obtaining hydrogen permeation parameters of a sample provided in an embodiment of the present invention.

[0020] Appendix Figure 3 This is a schematic diagram of the hydrogen distribution cloud map drawing method provided in an embodiment of the present invention.

[0021] Appendix Figure 4 This is a schematic diagram of the process for determining the equivalent hydrogen charging pressure provided in an embodiment of the present invention.

[0022] Appendix Figure 5 The temperature field diagrams for the welding process corresponding to the simulated weld overlay layers with thicknesses of 2mm, 3mm, and 4mm are provided for embodiments of the present invention.

[0023] Appendix Figure 6 The diagram shows the stress field of the welding process corresponding to the simulated weld overlay layers with thicknesses of 2mm, 3mm, and 4mm, provided for embodiments of the present invention.

[0024] Appendix Figure 7 The hydrogen distribution cloud maps corresponding to weld overlays with thicknesses of 2 mm, 3 mm, and 4 mm provided in the embodiments of the present invention are shown in (a) and (b) respectively. (a) is the hydrogen distribution cloud map corresponding to weld overlays with thicknesses of 2 mm, 3 mm, and 4 mm when only the microstructure inhomogeneity is considered. (b) is the hydrogen distribution cloud map corresponding to weld overlays with thicknesses of 2 mm, 3 mm, and 4 mm in service hydrogen pressure of 12 MPa.

[0025] Appendix Figure 8 The diagram shows the node hydrogen concentration values ​​extracted from the outside to the inside along the pipe wall thickness direction for weld overlays with thicknesses of 2 mm, 3 mm, and 4 mm, provided for embodiments of the present invention.

[0026] Appendix Figure 9 This is a schematic diagram of the quantitative mapping relationship between the weld overlay thickness and the equivalent hydrogen charging pressure provided in an embodiment of the present invention.

[0027] Appendix Figure 10 This is a schematic diagram of the method for predicting the weld overlay thickness of bimetallic composite pipes provided in an embodiment of the present invention.

[0028] Appendix Figure 11 This is a schematic diagram of the structure of the device for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, provided in an embodiment of the present invention.

[0029] Appendix Figure 12 This is a schematic diagram of the structure of the weld overlay thickness prediction device for bimetallic composite pipes provided in an embodiment of the present invention. Detailed Implementation

[0030] The present invention is not limited to the following embodiments, and the specific implementation can be determined according to the technical solution of the present invention and the actual situation.

[0031] Those skilled in the art will understand that, unless specifically stated otherwise, in the embodiments of the present invention, a "module" or "unit" refers to a computer program or part of a computer program that has a predetermined function and works together with other related parts to achieve a predetermined goal, and can be implemented wholly or partially using software, hardware (such as processing circuitry or memory), or a combination thereof. Similarly, a processor (or multiple processors or memory) can be used to implement one or more modules or units. Furthermore, each module or unit can be part of an overall module or unit that includes the functionality of that module or unit.

[0032] In addition, in the embodiments of the present invention, "multiple" refers to two or more, and "first" and "second" are used to distinguish descriptions and should not be construed as implying relative importance.

[0033] This invention provides a method, apparatus, and method / app for constructing a prediction model of weld overlay thickness for bimetallic composite pipes. The apparatus for constructing the prediction model and / or the prediction apparatus for weld overlay thickness of bimetallic composite pipes can be integrated into a computer device, which can be a server, a terminal, or other similar device; it can also be executed jointly by a terminal and a server. These examples should not be construed as limiting the invention.

[0034] The aforementioned terminals may include mobile phones, wearable smart devices, tablet computers, laptops, personal computers (PCs), and in-vehicle computers, etc., and this invention does not limit the number of such terminals.

[0035] The aforementioned server can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. This invention does not limit these features.

[0036] For example, computer equipment can be used to acquire hydrogen permeation parameters for different regions of bimetallic composite pipe samples with different weld overlay thicknesses. These parameters include the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the weld overlay. The welding process for bimetallic composite pipes with different weld overlay thicknesses can be simulated to determine the stress field generated during the welding process. For bimetallic composite pipes with different weld overlay thicknesses, the corresponding hydrogen permeation parameters and stress field can be used as initial and boundary conditions to simulate and obtain hydrogen distribution cloud maps for each weld overlay thickness. Based on the hydrogen distribution cloud map for each weld overlay thickness, the equivalent hydrogen charging pressure that can enter the base material can be determined, and a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure can be established to obtain a weld overlay thickness prediction model.

[0037] Based on this, the technical solution of the present invention will be described and explained below with reference to several examples.

[0038] Example 1: As shown in the attached document Figure 1 As shown in the figure, this invention discloses a method for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, comprising: Step S110: Obtain hydrogen permeation parameters for each region of the bimetallic composite pipe sample with different weld overlay thicknesses. The hydrogen permeation parameters include the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the weld overlay. Step S120: Simulate the welding process of bimetallic composite pipes with different weld overlay thicknesses, determine the stress field generated by the welding process, and use the corresponding hydrogen permeation parameters and stress field as initial and boundary conditions for bimetallic composite pipes with different weld overlay thicknesses to simulate and obtain hydrogen distribution cloud maps for each weld overlay thickness. Step S130: Based on the hydrogen distribution cloud map of each weld overlay thickness, determine the corresponding equivalent hydrogen charging pressure that can enter the base material, establish a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure, and obtain a weld overlay thickness prediction model.

[0039] In step S110 of this embodiment, the thickness of the weld overlay is selected and determined as needed. For example, the weld overlay thickness can be set to 2mm, 3mm, or 4mm. The hydrogen permeation parameters of each region of the bimetallic composite pipe corresponding to different weld overlay thicknesses are obtained. Specifically, a sample is set for each type of bimetallic composite pipe with different weld overlay thicknesses, and the hydrogen permeation parameters of each region of the sample are obtained. Each region of the sample includes the base material region and the weld overlay region. It should also be noted that the sample can be, but is not limited to, a homogeneous circular sample with a weld overlay and a base material. Its thickness and diameter are set as needed, for example, a diameter of 24mm and a thickness of 2mm.

[0040] It should also be noted that the hydrogen permeation parameters of each region of the sample can be obtained through hydrogen permeation tests. Specifically, high-pressure gas-phase hydrogen permeation tests can simulate the real service hydrogen-filling environment, thereby measuring parameters such as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of hydrogen-containing structural metal materials (base materials) during actual service. However, for materials with extremely low hydrogen diffusion coefficients, such as stainless steel and nickel-based alloys, the test cycle is too long. But if the sample thickness is reduced, the high-pressure hydrogen-filling environment becomes relatively dangerous. Therefore, for materials with FCC structures (weld overlays), electrochemical hydrogen permeation tests can be used to fill hydrogen using electrochemical methods, which can measure parameters such as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility.

[0041] In this embodiment, step S120 simulates the hydrogen distribution cloud map of each weld overlay thickness, and step S130 determines the equivalent hydrogen charging pressure that can enter the base material based on the hydrogen distribution cloud map of each weld overlay thickness. This can be achieved using finite element software, including ABAQUS simulation software.

[0042] In step S130 of this embodiment, a quantitative mapping relationship curve between the weld overlay thickness and the equivalent hydrogen charging pressure can be established using Origin plotting software, and a functional relationship model between different weld overlay thicknesses and equivalent hydrogen charging pressure can be fitted as a weld overlay thickness prediction model.

[0043] Furthermore, this embodiment can also establish a regular update mechanism to continuously expand or update the samples, and update the weld overlay thickness prediction model based on steps S110 to S130, so that the weld overlay thickness prediction results are more accurate.

[0044] This invention discloses a method for constructing a prediction model for the weld overlay thickness of bimetallic composite pipelines. It establishes a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure, fits the quantitative mapping relationship of "weld overlay thickness - equivalent hydrogen charging pressure," and forms a weld overlay thickness prediction model. Compared to methods such as machine learning, this process is simple, easy to operate, requires less computing equipment, and is low-cost. Furthermore, the constructed weld overlay thickness prediction model has high prediction accuracy and can be widely applied to the prediction of weld overlay thickness in bimetallic composite pipelines, providing a theoretical basis for the engineering design of high-pressure hydrogen transport composite pipelines.

[0045] Example 2: As shown in the attached document Figure 2 As shown, the embodiments of the present invention are further optimizations of the above embodiments, wherein obtaining the hydrogen permeation parameters of bimetallic composite pipe samples with different weld overlay thicknesses includes: Step S210: Obtain hydrogen permeation parameters for each region of the bimetallic composite pipe sample with different weld overlay thicknesses, obtain the hydrogen permeation curve of the sample base material, and perform linear fitting to obtain the slope of the hydrogen permeation curve. Calculate the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the base material using the steady-state permeation current density and the slope of the hydrogen permeation curve. Specifically: The hydrogen diffusion coefficient represents the migration rate of hydrogen in the parent material lattice and can be calculated using the Fourier method: right With time t Linear fitting was performed to obtain the slope of the hydrogen permeation curve. k The hydrogen diffusion coefficient is shown below: in, I t for t The osmotic current density at any given time; D is the steady-state osmotic current density; D is the hydrogen diffusion coefficient. L The thickness of the sample; k The slope of the hydrogen permeation curve can be determined by selecting two specific time points during the hydrogen permeation transient process. t 1 and t 2 Determine the corresponding osmotic current density I t1 and I t2 Calculate two The value is then used to determine the slope of the straight line, i.e., the slope of the hydrogen permeation curve, using the two points. Subsurface adsorbed hydrogen concentration represents the concentration of diffusible hydrogen entering the surface layer of the parent material, and can be calculated using the following formula: in, C 0 represents the subsurface adsorption hydrogen concentration; F It is Faraday's constant; Hydrogen solubility represents the ability of a substrate to dissolve hydrogen under a certain pressure, i.e., the concentration of hydrogen that the substrate can stably hold, and can be calculated using the following formula: Where S is the solubility of hydrogen; p This refers to the hydrogen transport pressure.

[0046] Step S220: Electrochemical hydrogen permeation experiments were conducted on the weld overlay of the sample using a Devanathane-Stachurski dual-electrolysis cell hydrogen permeation apparatus to obtain the hydrogen permeation curve of the weld overlay. The hydrogen diffusion coefficient was calculated using the time lag method. The average hydrogen concentration within the weld overlay was obtained through pre-charging with hydrogen and TDS thermal desorption mass spectrometry, determining the subsurface adsorbed hydrogen concentration and hydrogen solubility. Specifically: The hydrogen diffusion coefficient can be calculated using the following formula: Where D1 is the hydrogen diffusion coefficient; L The thickness of the sample; t L The time lag is the time delay. The concentration of hydrogen adsorbed on the subsurface can be calculated using the following formula: in, C v The average hydrogen concentration of the material; C 0 represents the subsurface adsorbed hydrogen concentration of the material; The density of the material is expressed in g·cm³. -3 ; Hydrogen solubility and hydrogen concentration can be calculated using the following formula: in, S For hydrogen solubility; p This refers to the hydrogen transport pressure.

[0047] It should also be noted that the average hydrogen concentration within the weld overlay of the sample was obtained through pre-hydrogen charging and TDS thermal desorption mass spectrometry. Specifically, the sample weld overlay was exposed to a simulated service hydrogen-charging environment. After hydrogen diffusion reached dynamic equilibrium, the average hydrogen concentration within the sample weld overlay was measured using a hydrogen content analyzer via TDS thermal desorption mass spectrometry. C v .

[0048] In this embodiment, a high-pressure gas-phase hydrogen permeation test is used to simulate the actual service hydrogen-filling environment, thereby measuring parameters such as the subsurface adsorbed hydrogen concentration, hydrogen diffusion coefficient, and hydrogen solubility of the base material (i.e., hydrogen-containing structural metal material) during actual service. However, for the weld overlay (i.e., materials with extremely low hydrogen diffusion coefficients such as stainless steel and nickel-based alloys), the test cycle is too long, and the high-pressure hydrogen-filling environment is relatively dangerous if the sample thickness is reduced. Therefore, in this embodiment, the sample is subjected to a high-pressure gas-phase hydrogen permeation test under hydrogen supply pressure to determine the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the base material. An electrochemical hydrogen permeation experiment is also carried out on the sample using a Devanathane-Stachurski dual-electrolysis cell hydrogen permeation device to obtain the hydrogen diffusion coefficient of the weld overlay. Then, the subsurface adsorbed hydrogen concentration of the weld overlay is obtained by pre-filling with hydrogen and TDS thermal desorption mass spectrometry, and the hydrogen solubility of the weld overlay is then calculated.

[0049] Example 3, as shown in the appendix Figure 3 As shown, the embodiments of the present invention are further optimizations of the above embodiments. They simulate the welding process of bimetallic composite pipes with different weld overlay thicknesses, determine the stress field generated during the welding process, and, for bimetallic composite pipes with different weld overlay thicknesses, use the corresponding hydrogen permeation parameters and stress field as initial and boundary conditions to simulate hydrogen distribution cloud maps for each weld overlay thickness, including: Step S310: For bimetallic composite pipes with different weld overlay thicknesses, establish corresponding three-dimensional finite element calculation models of bimetallic composite pipes. Because the weld overlay with a face-centered cubic structure has a low hydrogen diffusion coefficient, it can effectively prevent hydrogen from diffusing into the base material, thereby improving the hydrogen capacity of the base material. As the thickness of the weld overlay increases, the hydrogen pressure of the base material will also decrease, but the functional relationship is still unknown. Therefore, in this embodiment, a three-dimensional finite element calculation model (excluding circumferential weld) of the bimetallic composite pipe corresponding to different weld overlay thicknesses is first established using finite element software. The finite element software can be, but is not limited to, ABAQUS simulation software.

[0050] Step S320: Simulate the welding process for each bimetallic composite pipe three-dimensional finite element calculation model to obtain the temperature field of the corresponding welding process. This step can use the birth and death element technique in ABAQUS simulation software and the heat source subroutine in DFLUX to simulate the welding process, as detailed below: Heat source movement: Define the spatial distribution of heat flux density over time (Gaussian surface heat source or double ellipsoidal heat source) using DFLUX. Material is added layer by layer: Before simulating the welding process, all weld overlay units in the weld overlay layer are "killed," meaning they are all in a "killed" state. The first weld overlay unit set is then activated, and its heat convection and radiation processes during welding are simulated. After the first weld overlay is calculated, the second weld overlay unit set is activated, meaning it is in a "live" state. The previously activated first weld overlay unit set remains in a "live" state and can participate in subsequent heat convection and radiation calculations, while other weld overlay unit sets remain in a "killed" state. This process continues, activating, welding, and cooling the simulated weld overlays in the three-dimensional finite element calculation model of each bimetallic composite pipe according to the actual welding sequence, ultimately obtaining the temperature field results of the welding process. Thus, the welding process is simulated for three-dimensional finite element calculation models of bimetallic composite pipes with different weld overlay thicknesses, obtaining the corresponding temperature field of the welding process.

[0051] Step S330: The temperature field of all welding processes is checked by adjusting the parameters of the double ellipsoidal heat source and the cross-sectional shape and size of the simulated weld bead. In this step, quantitative processing is performed by continuously adjusting the parameters of the double ellipsoidal heat source and the shape and size of the molten pool in the simulated weld bead cross-section. This ensures that the calculated simulated weld beads closely approximate the actual weld bead shape and size, guaranteeing the reliability of the temperature field and the accuracy of the calculation results. This, in turn, ensures the accuracy of the subsequent stress field calculation results. This can be implemented using finite element software, including ABAQUS simulation software.

[0052] Step S340: The temperature field of the verified welding process is used as a predefined field and applied to the corresponding three-dimensional finite element calculation model of the bimetallic composite pipe. The welding residual stress generated during the welding process is sequentially coupled and calculated to form the stress field of the corresponding welding process. During actual welding, the weldment undergoes rigid body displacement due to heat. Therefore, when calculating the stress field, appropriate boundary conditions need to be added to the three-dimensional finite element model of the bimetallic composite pipe. Since the three-dimensional finite element model of the bimetallic composite pipe is half the size of the actual pipe, symmetry plane constraints and three-point constraints need to be applied to the two end sections of the model. Then, based on the temperature field calculation results, the temperature field results of each node changing over time are imported into the model. Subsequently, the blind hole method is used to test the stress distribution of the entire pipe to ensure the accuracy of the stress field calculation results. This can be achieved using finite element software, including ABAQUS simulation software.

[0053] Step S350: Using the hydrogen diffusion parameters and stress field corresponding to a certain thickness of weld overlay in a bimetallic composite pipe as initial and boundary conditions, calculate the corresponding hydrogen diffusion field, establish a hydrogen distribution cloud map, and traverse all thicknesses of weld overlay in bimetallic composite pipes to establish hydrogen distribution cloud maps for each thickness of weld overlay.

[0054] In this step, the hydrogen diffusion parameters and stress field corresponding to a certain thickness of the weld overlay of the bimetallic composite pipe are used as initial and boundary conditions to calculate the corresponding hydrogen diffusion field. Specifically, the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and solubility obtained from hydrogen permeation test and TDS test are used as initial conditions, and the stress field is used as a predefined field for hydrogen diffusion to perform stress-induced hydrogen diffusion coupling calculation to calculate the hydrogen diffusion field of the weld overlay.

[0055] This step can be implemented using finite element software, including ABAQUS simulation software.

[0056] It should also be noted that, in the simulation of the welding process of bimetallic composite pipes with different weld overlay thicknesses, the established weld pool movement path is consistent with the spiral weld bead of the pipe weld.

[0057] This embodiment achieves the fitting of the welding process corresponding to bimetallic composite pipes with different weld overlay thicknesses, and plots hydrogen distribution cloud maps, providing a basis for subsequently determining the maximum hydrogen concentration that can enter the base material (weak area).

[0058] Example 4: As shown in the appendix Figure 4 As shown, the embodiments of the present invention are further optimizations of the above embodiments, wherein the equivalent hydrogen charging pressure that can enter the base material is determined based on the hydrogen distribution cloud map of each weld overlay thickness, including: Step S410: Based on the hydrogen distribution cloud map of the weld overlay thickness, extract the maximum hydrogen concentration that can enter the base material; Step S420: The maximum hydrogen concentration that can enter the parent material is converted into the equivalent hydrogen charging pressure that can enter the parent material, wherein the conversion formula is as follows: in, P eq The equivalent hydrogen charging pressure required to enter the parent material, expressed in MPa; C max This represents the maximum hydrogen concentration within the parent material, expressed in ppm. S Hydrogen solubility in the weld overlay, in ppm atm -1 / 2 .

[0059] The maximum hydrogen concentration in the parent material can be obtained by using finite element software to extract the peak hydrogen concentration within the parent material unit set based on the hydrogen distribution cloud map. This peak hydrogen concentration is the maximum hydrogen concentration in the parent material.

[0060] Example 5: This example illustrates the process of constructing a prediction model for the weld overlay thickness of bimetallic composite pipes according to the present invention, as follows: (1) Set up samples of bimetallic composite pipes with different weld overlay thicknesses, where the weld overlay thicknesses are 2 mm, 3 mm and 4 mm; (2) Obtain the hydrogen permeation parameters of each sample, including the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the base material, and the hydrogen diffusion coefficient and hydrogen solubility of the weld overlay. (3) Using ABAQUS simulation software, establish corresponding three-dimensional finite element calculation models for bimetallic composite pipes with different weld overlay thicknesses; (4) Simulate the welding process of each bimetallic composite pipe using a three-dimensional finite element calculation model to obtain the temperature field of the corresponding welding process, as shown in the attached figure. Figure 5 As shown; (5) By adjusting the parameters of the double ellipsoidal heat source and the cross-sectional shape and size of the weld pool in the simulated weld overlay, the temperature field of all welding processes is checked. The checked temperature field of the welding process is used as a predefined field and applied to the corresponding three-dimensional finite element calculation model of the bimetallic composite pipe. The welding residual stress generated during the welding process is sequentially coupled and calculated to form the stress field of the corresponding welding process, as shown in the appendix. Figure 6 As shown; (6) Using the hydrogen diffusion parameters and stress field corresponding to a certain thickness of weld overlay in a bimetallic composite pipe as initial and boundary conditions, calculate the corresponding hydrogen diffusion field, establish a hydrogen distribution cloud map, and traverse all thicknesses of weld overlay in bimetallic composite pipes to establish hydrogen distribution cloud maps for each weld overlay thickness, as shown in the attached figure. Figure 7 As shown; (7) The hydrogen distribution cloud map was quantified to obtain the maximum hydrogen concentration that can enter the base material. The maximum hydrogen concentrations that can enter the base material for bimetallic composite pipes with weld overlay thicknesses of 2 mm, 3 mm, and 4 mm are 0.0057 ppm, 0.0017 ppm, and 0.0012 ppm, respectively. After conversion into equivalent hydrogen charging pressure values, they are 1.10674 MPa, 0.10066 MPa, and 0.04713 MPa, respectively. See attached figure for details. Figure 8 As shown; (8) Using Origin plotting software, establish a quantitative mapping curve between the weld overlay thickness and the equivalent hydrogen charging pressure, as shown in the attached figure. Figure 9 As shown, the prediction model for the weld overlay thickness is obtained; y=375.35983exp(-x / 0.34088)+0.04412 Where y is the equivalent hydrogen charging pressure of the base material; x is the predicted value of the weld overlay thickness; and exp() is an exponential function.

[0061] In the above model, the equivalent hydrogen charging pressure does not have a linear relationship with the increase of the weld overlay thickness. Therefore, in production, it can achieve the dual purpose of economy and practicality, determine the most suitable weld overlay thickness, and provide theoretical guidance for practical applications.

[0062] Example 6: As attached Figure 10 As shown in the figure, an embodiment of the present invention discloses a method for predicting the thickness of the weld overlay in bimetallic composite pipes, comprising: Step S510: Obtain the equivalent hydrogen charging pressure that can enter the parent material in the bimetallic composite pipe to be predicted; Step S520: Input the equivalent hydrogen charging pressure that can enter the base material into the weld overlay thickness prediction model to obtain the weld overlay thickness of the bimetallic composite pipe to be predicted. The weld overlay thickness prediction model is constructed using the weld overlay thickness prediction model construction method for bimetallic composite pipes.

[0063] Example 7: As attached Figure 11 As shown in the figure, an embodiment of the present invention discloses a device for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, comprising: The hydrogen permeation parameter acquisition unit acquires the hydrogen permeation parameters of each region of the bimetallic composite pipe sample with different weld overlay thicknesses. The hydrogen permeation parameters include the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the weld overlay. The hydrogen distribution cloud map drawing unit simulates the welding process of bimetallic composite pipes with different weld overlay thicknesses, determines the stress field generated during the welding process, and uses the corresponding hydrogen permeation parameters and stress field as initial and boundary conditions for bimetallic composite pipes with different weld overlay thicknesses to simulate and obtain hydrogen distribution cloud maps for each weld overlay thickness. The model building unit determines the equivalent hydrogen charging pressure that can enter the base material based on the hydrogen distribution cloud map of each weld overlay thickness, establishes a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure, and obtains a weld overlay thickness prediction model.

[0064] Example 8: As attached Figure 12 As shown, this embodiment of the invention discloses a device for predicting the thickness of the weld overlay in bimetallic composite pipes, comprising: The prediction data acquisition unit acquires the equivalent hydrogen charging pressure that can enter the parent material in the bimetallic composite pipe to be predicted. The prediction unit takes the equivalent hydrogen charging pressure that can enter the base material as input to the weld overlay thickness prediction model to obtain the weld overlay thickness of the bimetallic composite pipe to be predicted. The weld overlay thickness prediction model is constructed using the weld overlay thickness prediction model construction method for bimetallic composite pipes.

[0065] The above content is only a specific embodiment of the present invention, which has strong adaptability and implementation effect. However, the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be covered within the protection scope of the present invention. Therefore, equivalent changes made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for constructing a prediction model for the weld overlay thickness of bimetallic composite pipes, characterized in that, include: Hydrogen permeation parameters were obtained for each region of bimetallic composite pipe samples with different weld overlay thicknesses. The hydrogen permeation parameters included the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration, and hydrogen solubility of the weld overlay. The welding process of bimetallic composite pipes with different weld overlay thicknesses was simulated to determine the stress field generated during the welding process. For bimetallic composite pipes with different weld overlay thicknesses, the corresponding hydrogen permeation parameters and stress fields were used as initial and boundary conditions to simulate hydrogen distribution cloud maps for each weld overlay thickness. Based on the hydrogen distribution cloud map of each weld overlay thickness, the corresponding equivalent hydrogen charging pressure that can enter the base material is determined, and a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure is established to obtain the weld overlay thickness prediction model, as follows: y=375.35983exp(-x / 0.34088)+0.04412 Where y is the equivalent hydrogen charging pressure of the base material; x is the predicted value of the weld overlay thickness; and exp() is an exponential function.

2. The method for constructing a prediction model for weld overlay thickness in bimetallic composite pipes according to claim 1, characterized in that, Hydrogen permeation parameters were obtained for different regions of bimetallic composite pipe samples with varying weld overlay thicknesses, including: The sample parent material was subjected to a high-pressure gas phase hydrogen permeation test under hydrogen transport pressure to obtain the hydrogen permeation curve of the sample parent material. The curve was linearly fitted to obtain the slope of the hydrogen permeation curve. The hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the parent material were calculated using steady-state permeation current density and hydrogen permeation curve slope. Electrochemical hydrogen permeation experiments were conducted on the weld overlay of the sample using a Devanathane-Stachurski dual-electrolysis cell hydrogen permeation apparatus to obtain the hydrogen permeation curve of the weld overlay. The hydrogen diffusion coefficient was calculated using the time lag method. The average hydrogen concentration in the weld overlay of the sample was obtained by pre-charging hydrogen and TDS thermal desorption mass spectrometry, and the subsurface adsorbed hydrogen concentration and hydrogen solubility were determined.

3. The method for constructing a prediction model for weld overlay thickness of bimetallic composite pipes according to claim 1 or 2, characterized in that, The welding process of bimetallic composite pipes with different weld overlay thicknesses was simulated to determine the stress field generated during the welding process. For bimetallic composite pipes with different weld overlay thicknesses, the corresponding hydrogen permeation parameters and stress fields were used as initial and boundary conditions to simulate hydrogen distribution cloud maps for each weld overlay thickness, including: For bimetallic composite pipes with different weld overlay thicknesses, a corresponding three-dimensional finite element calculation model for bimetallic composite pipes is established. The welding process was simulated for each three-dimensional finite element calculation model of bimetallic composite pipes to obtain the temperature field of the corresponding welding process. The temperature field of the welding process is used as a predefined field and applied to the corresponding three-dimensional finite element calculation model of the bimetallic composite pipe. The welding residual stress generated during the welding process is sequentially coupled and calculated to form the stress field of the corresponding welding process. Using the hydrogen diffusion parameters and stress field corresponding to a bimetallic composite pipe with a certain weld overlay thickness as initial and boundary conditions, the corresponding hydrogen diffusion field is calculated, and a hydrogen distribution cloud map is established. This process is repeated for all bimetallic composite pipes with different weld overlay thicknesses to establish hydrogen distribution cloud maps for each weld overlay thickness.

4. The method for constructing a prediction model for weld overlay thickness in bimetallic composite pipes according to claim 3, characterized in that, It also includes checking the temperature field of all welding processes by adjusting the parameters of the double ellipsoidal heat source and simulating the cross-sectional shape and size of the weld pool in the weld bead.

5. The method for constructing a prediction model for weld overlay thickness of bimetallic composite pipes according to claim 3, characterized in that, The welding process of each bimetallic composite pipe was simulated using the birth and death element technique in ABAQUS simulation software and the heat source subroutine in DFLUX.

6. The method for constructing a prediction model for weld overlay thickness of bimetallic composite pipes according to claim 1, 2, 4, or 5, characterized in that, Based on the hydrogen distribution cloud map of each weld overlay thickness, the corresponding equivalent hydrogen charging pressure that can penetrate the base material is determined, including: Based on the hydrogen distribution cloud map of the weld overlay thickness, the maximum hydrogen concentration that can enter the base material is extracted; The maximum hydrogen concentration that can enter the parent material is converted into the equivalent hydrogen charging pressure that can enter the parent material, and the conversion formula is as follows: in, P eq To achieve the equivalent hydrogen charging pressure required to enter the parent material; C max This represents the maximum hydrogen concentration within the parent material. S This represents the hydrogen solubility in the weld overlay.

7. The method for constructing a prediction model for weld overlay thickness of bimetallic composite pipes according to claim 2 or 4, characterized in that, The test specimen is a homogeneous circular specimen with a diameter of 24 mm and a thickness of 2 mm, formed by processing the weld overlay and the base material.

8. A method for predicting the thickness of the weld overlay in bimetallic composite pipes, characterized in that, include: Obtain the equivalent hydrogen charging pressure that can enter the parent material in the bimetallic composite pipe to be predicted; The equivalent hydrogen charging pressure that can enter the base material is input into the weld overlay thickness prediction model to obtain the weld overlay thickness of the bimetallic composite pipe to be predicted, wherein the weld overlay thickness prediction model is constructed using the model construction method described in any one of claims 1 to 7.

9. A model building apparatus for predicting the weld overlay thickness of bimetallic composite pipes using the model building method as described in any one of claims 1 to 7, characterized in that, include: The hydrogen permeation parameter acquisition unit acquires the hydrogen permeation parameters of each region of the bimetallic composite pipe sample with different weld overlay thicknesses. The hydrogen permeation parameters include the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the base material, as well as the hydrogen diffusion coefficient, subsurface adsorbed hydrogen concentration and hydrogen solubility of the weld overlay. The hydrogen distribution cloud map drawing unit simulates the welding process of bimetallic composite pipes with different weld overlay thicknesses, determines the stress field generated during the welding process, and uses the corresponding hydrogen permeation parameters and stress field as initial and boundary conditions for bimetallic composite pipes with different weld overlay thicknesses to simulate and obtain hydrogen distribution cloud maps for each weld overlay thickness. The model building unit determines the equivalent hydrogen charging pressure that can enter the base material based on the hydrogen distribution cloud map of each weld overlay thickness, establishes a quantitative mapping relationship curve between weld overlay thickness and equivalent hydrogen charging pressure, and obtains a weld overlay thickness prediction model.

10. A device for predicting the thickness of weld overlay in bimetallic composite pipes, characterized in that, include: The prediction data acquisition unit acquires the equivalent hydrogen charging pressure that can enter the parent material in the bimetallic composite pipe to be predicted. The prediction unit inputs the equivalent hydrogen charging pressure that can enter the base material into the weld overlay thickness prediction model to obtain the weld overlay thickness of the bimetallic composite pipe to be predicted, wherein the weld overlay thickness prediction model is constructed using the model construction method described in any one of claims 1 to 7.

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