Pipeline internal corrosion modeling method based on curvature-containing random surface and application of pipeline internal corrosion modeling method

Abstract

The invention discloses a curvature-containing random surface pipeline internal corrosion modeling method and application. The method comprises the steps that the geometric dimension of a pipeline is determined; generating a parameterized curved surface, and establishing a curvature-containing random surface model by setting an N value, a beta value, a random function item and a parameterized curved surface node; and the surface is attached to the inner wall of the pipeline, the generated random surface is attached to the inner wall of the pipeline through operation, pipeline corrosion cutting is conducted, and corrosion parameters are obtained. By introducing the random surface model with curvature and adopting the combination of spatial frequency resolution, spectral index and random function, the corrosion morphology of the inner surface of the pipeline is accurately simulated, the macroscopic pipeline curvature and the microscopic surface fluctuation can be reflected, the model parameters can be flexibly adjusted, the requirements in different corrosion environments can be met, and the method is suitable for large-scale popularization and application. Scientific support can be provided for corrosion evaluation, design optimization and maintenance decision making of pipelines of different shapes and material types, and the method is suitable for pipeline corrosion prediction and analysis in the industries of petroleum, natural gas, chemical engineering and the like.

Description

Technical Field

[0001] This invention relates to the field of pipeline corrosion modeling technology, specifically to a method and application for modeling corrosion inside pipelines with random surfaces containing curvature. Background Technology

[0002] Pipeline corrosion is a major challenge in modern industry, especially in sectors such as oil, gas, chemicals, and water supply. Corrosion not only affects pipeline operating efficiency but can also lead to serious safety accidents such as leaks and ruptures, threatening the environment and human health. Therefore, accurately predicting and assessing pipeline damage has become a key research topic for ensuring safe pipeline operation and extending pipeline service life. The corrosion process itself is complex and influenced by multiple factors, including pipeline material, fluid properties, external environment, and pipeline surface condition. The interaction of these factors makes the corrosion process highly nonlinear and uncertain, increasing the difficulty of corrosion modeling.

[0003] Existing corrosion models sometimes rely on the assumption of a uniform surface, neglecting the geometric variations and randomness of the pipeline surface. For example, existing technology CN117074283A discloses a prediction model for the uniform corrosion rate of water pipelines that considers interactions. This model, based on a three-level, four-factor orthogonal experiment in a high-temperature, high-pressure dynamic reactor and combined with multiple linear regression, calculates the uniform corrosion rate of water pipelines by considering the effects of temperature, pressure, dissolved oxygen concentration, flow rate, and the interaction between temperature and dissolved oxygen concentration. Other models are based on empirical formulas or simplified theoretical models, which, while providing some reference under certain specific conditions, are generally unable to effectively address the complexity and randomness of the corrosion process. A typical example is the WM fractal function model. The WM fractal function model assumes that the corroded surface exhibits fractal characteristics, and its specific expression is:

[0004] In this model, Gn, γ, D, Bn, and An are parameters related to the morphology of the corroded surface. γ controls the scale variation of the fractal, while the trigonometric function terms reflect the local fluctuations of the corroded surface. The advantage of this model is its ability to describe the self-similarity of the surface through fractal functions, thus simulating the complex texture of the corroded surface to some extent. However, this model has significant limitations. The WM fractal function assumes that the corroded surface follows certain regularities and self-similarity, but in practical applications, corroded surfaces often exhibit more complex randomness and irregularities. For example, the pipe surface may develop irregular features such as cracks, local depressions, or corrosion pits due to factors such as stress and temperature. These irregularities are difficult to capture effectively in the WM fractal function. Furthermore, this model ignores the attenuation effect of high-frequency fluctuations, making it unable to accurately reflect the details of the corrosion evolution process, especially when high-frequency fluctuations have a significant impact on the corrosion process.

[0005] Traditional surface morphology modeling methods are typically based on simple statistical models or fitting experimental data, which struggle to accurately describe the randomness and nonlinearity of complex surfaces. To more accurately simulate corrosion processes within pipelines, a corrosion modeling method that can simultaneously consider the effects of surface randomness and curvature is urgently needed. Summary of the Invention

[0006] This invention provides a pipeline corrosion modeling method and its application. This method comprehensively considers the influence of pipeline surface curvature and random surface irregularities on the corrosion process, and can accurately simulate local material loss caused by fluid flow. By using a series of mathematical expressions in COMSOL Multiphysics software, the corrosion of the inner surface of the pipeline can be simulated.

[0007] The technical solution adopted by this invention to solve its technical problem is as follows: A method for modeling corrosion inside a random surface pipe with curvature, comprising the following steps: Step S100: Determine the pipe geometry, such as pipe diameter and wall thickness; Step S200: Generate a parametric surface using COMSOL Multiphysics software. Establish a random surface model with curvature by setting the N value, β value, random function term, and parametric surface nodes. The specific expression is as follows:

[0008] In the formula: A is the amplitude scale factor, which determines the intensity of the overall surface fluctuations; N is the spatial frequency resolution, used to determine the level of detail of the random surface. A larger N can provide higher accuracy of surface fluctuations; m and n are the spatial frequencies. It is the amplitude of each frequency, generated by a random function, and different surface features can be simulated by the amplitude of different frequencies; It is the phase angle, which follows a random function uniformly distributed in [-π,π], thus avoiding the periodic symmetry of surface fluctuations; It is the global curvature, used to describe the overall geometry of a random surface; x and y are spatial coordinates. In step S300, the surface is attached to the inner wall of the pipe. Through operations such as rotation, proportional scaling and displacement, the generated random surface is attached to the inner wall of the pipe to perform pipe corrosion cutting and obtain corrosion parameters.

[0009] Furthermore, a high-fidelity realistic damage model was created by cutting the solid in the geometry module of the COMSOL Multiphysics software.

[0010] Furthermore, the measurement function in the geometry module of COMSOL Multiphysics software was used to obtain the corrosion perimeter, corrosion area, and corrosion depth of the pipe surface.

[0011] Furthermore, by adjusting the curvature in the x-direction and / or y-direction, a suitable curvature variation of the corroded surface can be obtained.

[0012] Furthermore, after obtaining the parameters in step 300, the following steps are also included: constructing multiple cases of damage to the inner wall of large-diameter pipes to ensure that the damage depth is constant and the damage area varies from large to small to simulate different degrees of damage; collecting dynamic feedback signals when the pipe actuator is working through high-precision sensors, and using wavelet packet decomposition technology to decompose the signals into multiple scales and extract the features of each frequency band; calculating the energy distribution of each frequency band based on the decomposed signals, and defining the damage index as the ratio of the energy of the key frequency band to the total energy, which is used to quantify the degree of damage to the inner wall of the pipe.

[0013] Furthermore, in step S200, the random amplitude is used... The fluctuation intensity of each frequency component is determined by a combination of a random function following a standard normal distribution and a frequency decay function, i.e., the amplitude. Generate using the following formula:

[0014] in: It is a random function that follows a standard normal distribution and is used to simulate the randomness of surface roughness. The characteristics of the standard normal distribution ensure that the random generation of amplitude has a natural distribution law, which conforms to the characteristics of random fluctuations of actual corroded surfaces.

[0015] Furthermore, the random function that follows a standard normal distribution The specific formula is:

[0016] In the formula, , Let m represent the expected value and variance, respectively. , Let n represent the expected value and variance, respectively. Let represent the correlation coefficient between m and n, satisfying -1 ≤ ρ ≤ 1. Wherein, =0: m and n are independent; >0: Positive correlation (n tends to increase as m increases); <0: Negative correlation (n tends to decrease as m increases).

[0017] It is a frequency decay function used to represent the decay of high-frequency fluctuations.

[0018] Furthermore, the frequency attenuation function The specific formula is:

[0019] In the formula, It is a spectral index used to control the attenuation rate of high-frequency roughness. A larger one... A higher value will cause high-frequency components to decay faster, resulting in a smoother surface; a lower value... The value will retain more high-frequency components, resulting in a rougher surface that can better simulate more complex and detailed corrosion morphologies. By adjusting... The value can be optimized based on different corrosion types (such as pitting, uniform corrosion, or localized damage) to make it more consistent with the corrosion characteristics in actual applications.

[0020] Further, the phase angle is generated. The uniformly distributed random function is expressed as:

[0021] Furthermore, a random seed is used to fix the generation process of the random function.

[0022] Furthermore, by adjusting parameters A, B, C, β, and N, the curvature and local fluctuations of the surface can be further adjusted.

[0023] This invention also provides an application of the above-described method for modeling corrosion inside pipes with a random surface containing curvature, which is used in pipe corrosion morphology scenarios such as pitting corrosion and erosion corrosion.

[0024] Compared with the prior art, the present invention has at least one of the following beneficial effects: (1) By introducing a global curvature term to simulate the curvature effect of the inner surface of the pipe, the influence of surface curvature on corrosion distribution can be accurately reflected, thereby improving the accuracy of corrosion prediction. (2) The amplitude term is generated by combining Gaussian distribution and frequency decay function, which can effectively simulate random fluctuations and high-frequency decay phenomena on the pipe surface, thus better reflecting the actual corrosion situation; (3) The mathematical model used is relatively simple and easy to implement. It can be numerically calculated and analyzed by simulation software such as COMSOL Multiphysics and is suitable for corrosion prediction of various pipeline systems. (4) By introducing a random surface model with curvature, and employing a combination of spatial frequency resolution, spectral index, and random functions, the corrosion morphology of the inner surface of the pipeline was accurately simulated. This method not only reflects the macroscopic pipeline curvature and microscopic surface fluctuations, but also allows for flexible adjustment of model parameters to adapt to the needs of different corrosion environments. Through simulation analysis using COMSOL Multiphysics software, scientific support can be provided for pipeline corrosion assessment, design optimization, and maintenance decisions. Furthermore, it can adapt to different pipeline shapes and material types, making it suitable for pipeline corrosion prediction and analysis in industries such as petroleum, natural gas, and chemicals. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the process for modeling corrosion inside a random surface pipe with curvature provided by the present invention; Figure 2 This is a schematic diagram illustrating the definition of spatial frequency resolution and spectral index parameters provided by the present invention; Figure 3 This is a schematic diagram of adding a random function provided by the present invention; Figure 4 This is a schematic diagram of the defined parameterized surface provided by the present invention; Figure 5 This is a schematic diagram of a random surface with curvature provided by the present invention; Figure 6 This is a schematic diagram of the random surface fitting with the inner wall of the pipe provided by the present invention; Figure 7 This is a schematic diagram of the pipeline corrosion morphology model provided by the present invention; Figure 8 This is a schematic diagram of the actual corrosion morphology of the pipeline provided by the present invention; Figure 9 This is a diagram of pipeline corrosion parameters provided by the present invention; Figure 10 This is a schematic diagram of curvature adjustment in various directions provided by the present invention; Figure 11 This is the damage index diagram provided by the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Reference Figure 1 A method for modeling corrosion inside pipes with curvature and random surfaces includes the following steps: Step S100: Determine the pipe geometry, such as pipe diameter and wall thickness; Step S200: Generate a parametric surface using COMSOL Multiphysics software. Establish a random surface model with curvature by setting the N value, β value, random function term, and parametric surface nodes. The specific expression is as follows:

[0028] In the formula: A is the amplitude scale factor, which determines the intensity of the overall surface fluctuations; N is the spatial frequency resolution, used to determine the level of detail of the random surface. A larger N can provide higher accuracy of surface fluctuations; m and n are the spatial frequencies. It is the amplitude of each frequency, generated by a random function, and different surface features can be simulated by the amplitude of different frequencies; It is the phase angle, which follows a random function uniformly distributed in [-π,π], thus avoiding the periodic symmetry of surface fluctuations; It is the global curvature, used to describe the overall geometry of a random surface; x and y are spatial coordinates. In step S300, the surface is attached to the inner wall of the pipe. Through operations such as rotation, proportional scaling and displacement, the generated random surface is attached to the inner wall of the pipe to perform pipe corrosion cutting and obtain corrosion parameters.

[0029] Accurate simulation of corroded surfaces has always been a challenge and a key issue. The applicant has also conducted some research on this, as seen in the patent technology with application number CN202510848386.X. By combining Fourier series, which effectively describes the periodic roughness characteristics of the surface, with a polynomial function, which describes the overall deformation trend of the surface, corroded surfaces can be well characterized, improving simulation results. This invention also introduces a global curvature term... This method simulates the curvature effect of the inner surface of a pipeline, thereby accurately reflecting the influence of the pipeline's surface curvature on corrosion distribution and improving the accuracy of pipeline corrosion prediction.

[0030] Further, in step S200, the random amplitude This is an important component of surface fluctuations in this invention, determining the fluctuation intensity of each frequency component. The specific calculation method uses a combination of a random function following a standard normal distribution and a frequency decay function, i.e., the amplitude. Generate using the following formula:

[0031] in: It is a random function that follows a standard normal distribution and is used to simulate the randomness of surface roughness. The characteristics of the standard normal distribution ensure that the random generation of amplitude has a natural distribution law, which conforms to the characteristics of random fluctuations of actual corroded surfaces.

[0032] Furthermore, the random function that follows a standard normal distribution The specific formula is:

[0033] In the formula, , Let m represent the expected value and variance, respectively. , Let n represent the expected value and variance, respectively. Let represent the correlation coefficient between m and n, satisfying -1 ≤ ρ ≤ 1. Wherein, =0: m and n are independent; >0: Positive correlation (n tends to increase as m increases); <0: Negative correlation (n tends to decrease as m increases).

[0034] It is a frequency decay function used to represent the decay of high-frequency fluctuations.

[0035] Furthermore, the frequency attenuation function The specific formula is:

[0036] In the formula, It is a spectral index used to control the attenuation rate of high-frequency roughness. A larger one... A higher value will cause high-frequency components to decay faster, resulting in a smoother surface; a lower value... The value will retain more high-frequency components, resulting in a rougher surface that can better simulate more complex and detailed corrosion morphologies. By adjusting... The value can be optimized based on different corrosion types (such as pitting, uniform corrosion, or localized damage) to make it more consistent with the corrosion characteristics in actual applications.

[0037] Further, the phase angle is generated. The uniformly distributed random function is expressed as:

[0038] Furthermore, to ensure that the same input parameters generate the same random surface, a random seed can be used to fix the generation process of the random function. Specifically, in the COMSOL Multiphysics software, a random seed is selected when generating the random function, which can then ensure that the random surface generated each time is fixed.

[0039] Furthermore, in the pipeline corrosion modeling process, after generating a corrosion surface with randomness and curvature effects, the next step is to fit this surface to the internal geometry of the pipeline. This step is crucial to ensuring the accuracy and realism of the corrosion model, as the actual corrosion process is strongly influenced by the pipeline geometry. To accurately align the generated random surface with the pipeline's inner wall, a series of geometric transformations and adjustments are typically required to ensure that the final corrosion surface accurately reflects the actual pipeline conditions. Rotation, proportional scaling, and displacement: By rotating, scaling, and displacing, the generated random surface can be adjusted to fit the pipeline's inner wall. This ensures that the corrosion surface accurately conforms to the pipeline model.

[0040] Furthermore, by adjusting parameters A, B, C, β, and N, the surface curvature and local fluctuations can be further tuned. These parameters control the surface properties from macroscopic to microscopic scales to better simulate the real process of corrosion within pipes.

[0041] Furthermore, a high-fidelity realistic damage model can be created by cutting the solid in the geometry module of the COMSOL Multiphysics software; if a more regular erosion boundary is required, a regular erosion boundary can be created by cutting the solid in the geometry module of the COMSOL Multiphysics software, thereby obtaining the desired boundary shape.

[0042] Furthermore, in the process of pipeline corrosion modeling, acquiring and analyzing key parameters of the pipeline's inner surface is a crucial step in assessing the degree of corrosion and predicting pipeline service life. In the method of this invention, the measurement function in the geometry module of COMSOL Multiphysics software can be used to effectively acquire important parameters such as the corrosion perimeter, corrosion area, and corrosion depth of the pipeline surface, thereby providing accurate data support for further analysis and optimization of pipeline corrosion protection.

[0043] Furthermore, by adjusting the curvature in the x-direction and / or y-direction, a suitable curvature variation can be obtained. This method can effectively reflect the corrosion characteristics in different directions within the pipeline, providing more accurate corrosion modeling results.

[0044] Furthermore, the parameters obtained in step 300 can be used as the following evaluation indicators: to construct various large-diameter pipe inner wall damage cases, ensuring that the damage depth is constant and the damage area varies from large to small, in order to simulate different damage degrees; to collect dynamic feedback signals when the pipe actuator is working through high-precision sensors, and to perform multi-scale decomposition of the signals using wavelet packet decomposition technology to extract the features of each frequency band; to calculate the energy distribution of each frequency band based on the decomposed signals, and to define the damage index as the ratio of the key frequency band energy to the total energy, in order to quantify the degree of damage to the inner wall of the pipe.

[0045] The following description uses a pipeline erosion corrosion scenario as an example. During erosion corrosion, high fluid velocity exerts a strong mechanical effect on the pipeline surface, typically accelerating localized corrosion. This method comprehensively considers the influence of pipeline surface curvature and random surface irregularities on the corrosion process, accurately simulating localized material loss caused by fluid flow. The specific steps of this method in the erosion corrosion scenario include: Step 1, refer to Figure 2 Define the spatial frequency resolution and spectral index parameters.

[0046] In pipeline corrosion modeling, spatial frequency resolution N and spectral index β are two crucial parameters that directly affect the detail, accuracy, and realism of the generated random surfaces. Fine-tuning these two parameters allows for the capture of corrosion features at different levels in the simulation and the simulation of different types of corrosion processes as needed, thereby improving the model's accuracy and applicability.

[0047] Spatial frequency resolution (N): Controls the detail and accuracy of the model. A larger N value can capture higher frequency surface fluctuations, providing higher resolution, but it also increases computational complexity. This parameter usually needs to be selected based on the required simulation accuracy; in COMSOL Multiphysics software, N=20 is set.

[0048] Spectral index (β): Controls the amplitude decay rate. A larger β value results in faster decay of high-frequency components and a smoother surface; a smaller β value retains more high-frequency fluctuations, resulting in a rougher surface. This parameter can be adjusted to simulate different types of corrosion damage (such as smoother or rougher corrosion surfaces). In COMSOL Multiphysics software, b represents the spectral index, and b=1.8 is set.

[0049] Step 2, refer to Figure 3Add two random functions to COMSOL Multiphysics software. and .

[0050] In COMSOL Multiphysics software, two random functions are introduced. and These two functions can add necessary randomness to the corrosion modeling of the inner surface of pipelines, thereby simulating the microscopic irregularities present on the corroded surface in a real environment. The introduction of these two functions enables the model to more accurately reflect the surface fluctuation characteristics and changes at different locations during pipeline corrosion.

[0051] random function This function follows a normal distribution and is used to generate amplitude. It determines the intensity of each frequency component.

[0052] Phase angle This function is a random function that follows a uniform distribution and is defined in the interval [−π / 2, π / 2]. It controls the phase of fluctuations at different frequencies, so that each frequency fluctuation has a different relative offset in space.

[0053] Furthermore, to ensure that the same input parameters generate the same random surface, a random seed can be used to fix the generation process of the random function. In COMSOL Multiphysics software, g1(m,n) represents the random function, and u1(m,n) represents the phase angle.

[0054] Step 3, refer to Figure 4 and Figure 5 Define a parametric surface.

[0055] In the modeling of corrosion within pipelines, accurately reproducing the changes in corrosion morphology on the pipeline surface is crucial. To achieve this goal, the method of this invention utilizes the geometry module of COMSOL Multiphysics software to construct a randomized corrosion surface by adding parametric surface nodes. The core of this step is to model the corrosion surface as a dynamic surface that varies with time or space. By precisely defining the Z-coordinate expression, a surface with randomness and curvature effects is generated. In COMSOL Multiphysics software, s1 and s2 represent spatial coordinates, with A=0.01, B=0.6, C=0.6, and s1 and s2 defined in the interval [−0.5, 0.5]. The specific formula is as follows: Z=0.01*sum(sum(if((m!=0)||(n!=0),((m^2+n^2)^(-b / 2))*g1(m,n)*cos(2*pi*(m*s1+n*s2)+u1(m,n)),0),m,-N,N),n,-N,N)+ 0.6*s1^2+0.6*s2^2 In the formula: 0.01 is a scaling factor that affects the final shape and undulation; decreasing this value will flatten the surface. The term (m^2+n^2)^(-b / 2) represents the attenuation factor for high-frequency fluctuations, weighted according to the values ​​of m and n. b is a parameter controlling the attenuation, determining the impact of distant control points on the final result. The cosine function term controls the surface fluctuation pattern, adjusting the periodicity and spatial distribution of the fluctuations through s1, s2, and the phase angle. The part 0.6*s1^2+0.6*s2^2 includes an overall adjustment to the height value originally generated by summation and an increase in global offset, used to simulate the overall curvature change of the surface.

[0056] Step 4, refer to Figure 6 , Figure 7 and Figure 8 Adjust the random surface to fit the inside of the pipe.

[0057] In pipeline corrosion modeling, after generating a corrosion surface with randomness and curvature effects, the next step is to fit this surface to the internal geometry of the pipeline. This step is crucial for ensuring the accuracy and realism of the corrosion model, as the actual corrosion process is strongly influenced by the pipeline geometry. To precisely align the generated random surface with the pipeline's inner wall, a series of geometric transformations and adjustments are typically required to ensure that the final corrosion surface accurately reflects the actual conditions of the pipeline.

[0058] Rotation, scaling, and displacement: By rotating, scaling, and displacing, the generated random surface can be adjusted to fit the inner wall of the pipe. This ensures that the corroded surface accurately conforms to the pipe model.

[0059] Furthermore, by adjusting parameters A, B, C, β, and N, the surface curvature and local fluctuations can be further tuned. These parameters control the surface properties from macroscopic to microscopic scales to better simulate the real process of corrosion within pipes.

[0060] Furthermore, if a more regular erosion boundary is required, a regular erosion boundary can be created by cutting the solid in the geometry module, thereby obtaining the desired boundary shape.

[0061] Step 5: Refer to Figure 9 Get the parameters.

[0062] In pipeline corrosion modeling, acquiring and analyzing key parameters of the pipeline's inner surface is a crucial step in assessing corrosion levels and predicting pipeline lifespan. The method of this invention utilizes the measurement function in the geometry module of COMSOL Multiphysics software to effectively acquire important parameters such as corrosion perimeter, corrosion area, and corrosion depth of the pipeline surface, thereby providing accurate data support for further analysis and optimization of pipeline corrosion protection.

[0063] As an example, the method for modeling corrosion within a pipe with a random surface containing curvature is based on the assumption that scouring corrosion only requires adjusting the curvature in the x-direction. (See reference...) Figure 10 The curvature can be adjusted according to the actual situation. If only the curvature needs to be adjusted in the x-direction, it can be achieved by increasing s1^2 alone; if the curvature needs to be adjusted in the y-direction, it can be achieved by increasing s2^2; if both the x and y directions need to be adjusted, it can be achieved by increasing s1^2 + s2^2 to obtain a suitable curvature change. This method can effectively reflect the corrosion characteristics in different directions within the pipeline and provide more accurate corrosion modeling results.

[0064] The acquired parameters can be used as the following evaluation indicators: to construct various large-diameter pipe inner wall damage cases, ensuring that the damage depth is constant and the damage area varies from large to small, in order to simulate different damage degrees; to collect dynamic feedback signals when the pipe actuator is working through high-precision sensors, and to perform multi-scale decomposition of the signals using wavelet packet decomposition technology to extract the features of each frequency band; to calculate the energy distribution of each frequency band based on the decomposed signals, and to define the damage index as the ratio of the energy of the key frequency band to the total energy, in order to quantify the degree of damage to the inner wall of the pipe.

[0065] Under the condition of constant depth, the damage index is positively correlated with the area of ​​action, and its trend follows a linear growth pattern; the results are as follows. Figure 11 As shown. It should be noted that the curves obtained in the experiment are only the results of data fitting under specific conditions. In practical applications, there may be various functional relationships, including but not limited to nonlinear relationships such as exponential functions, logarithmic functions, or piecewise functions. The specific correlation needs to be further verified based on the actual working parameters.

[0066] The present invention also provides an application of a method for modeling corrosion inside pipes with curvature on random surfaces, which is used in pipe corrosion morphology scenarios such as pitting corrosion and erosion corrosion.

[0067] Through the above description of the embodiments, the method provided by the present invention can help those skilled in the art to achieve accurate modeling of corrosion morphology inside pipelines, especially in the modeling of stochastic surfaces considering curvature effects. This provides reliable numerical support for pipeline corrosion assessment, life prediction, and protection design, and has broad application prospects and technical value.

[0068] The above embodiments have provided a detailed description of the present invention, but the content described is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent variations and improvements made within the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A method for modeling corrosion inside pipes with random surfaces containing curvature, characterized in that, The steps include: Step S100: Determine the pipe geometry, including pipe diameter and wall thickness; Step S200: Generate a parametric surface using COMSOL Multiphysics software. Establish a random surface model with curvature by setting the N value, β value, random function term, and parametric surface nodes. The specific expression is as follows: ； In the formula: A is the amplitude scaling factor; N is the spatial frequency resolution; m and n are the spatial frequencies; It is the amplitude at each frequency; It is the phase angle, which obeys [ , A uniformly distributed random function; It is the global curvature used to describe the overall geometry of a random surface; x and y are spatial coordinates; In step S300, the surface is attached to the inner wall of the pipe. By rotating, scaling proportionally, and displacing, the generated random surface is attached to the inner wall of the pipe to perform pipe corrosion cutting and obtain corrosion parameters.

2. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 1, characterized in that, High-fidelity realistic damage models are created by cutting solids in the geometry module of COMSOL Multiphysics software.

3. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 1, characterized in that, The measurement function in the geometry module of COMSOL Multiphysics software is used to obtain the corrosion perimeter, corrosion area, and corrosion depth of the pipe surface.

4. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 1, characterized in that, After obtaining the parameters in step 300, the following steps are also included: constructing multiple cases of damage to the inner wall of large-diameter pipes, ensuring that the damage depth is constant and the damage area varies from large to small to simulate different degrees of damage; collecting dynamic feedback signals when the pipe actuator is working through high-precision sensors, and using wavelet packet decomposition technology to decompose the signals into multiple scales and extract the features of each frequency band; calculating the energy distribution of each frequency band based on the decomposed signals, and defining the damage index as the ratio of the energy of the key frequency band to the total energy, which is used to quantify the degree of damage to the inner wall of the pipe.

5. The method for modeling corrosion inside pipes with curvature on random surfaces according to any one of claims 1-4, characterized in that, In step S200, random amplitude The specific calculation method uses a combination of a random function that follows a standard normal distribution and a frequency decay function, i.e., the amplitude. Generate using the following formula: ； in: It is a random function that follows a standard normal distribution and is used to simulate the randomness of surface roughness; It is a frequency decay function used to represent the decay of high-frequency fluctuations.

6. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 5, characterized in that, Use a random seed to fix the generation process of the random function.

7. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 5, characterized in that, The specific formula for the random function that follows a standard normal distribution is: ； In the formula, , Let m represent the expected value and variance, respectively. , Let n represent the expected value and variance, respectively. Let m represent the correlation coefficient between m and n, satisfying -1 ≤ ρ ≤ 1.

8. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 5, characterized in that, The frequency attenuation function The specific formula is: ； In the formula, It is a spectral index.

9. The method for modeling corrosion inside pipes with curvature on random surfaces according to claim 8, characterized in that, The curvature and local fluctuations of the surface can be adjusted by modifying parameters A, B, C, β, and N.

10. An application of the method for modeling corrosion inside a pipe with a random surface containing curvature according to any one of claims 1-9, characterized in that, Used in pipeline corrosion morphology scenarios such as pitting corrosion and erosion corrosion.

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