A method for generating random fields for nonstationary corrosion pipelines through trend texture reconstruction

Abstract

This invention discloses a method for generating random fields for non-stationary corrosion pipelines through trend texture reconstruction, relating to the field of steel pipe corrosion morphology modeling. The method first performs 3D scanning and filtering on a real corroded pipeline to obtain a pure corrosion height field, which is then decoupled into a macroscopic non-stationary trend field and a microscopic stationary texture field. Next, a database mapping relationship between microscopic roughness parameters and power spectral density is constructed, and a simulated stationary texture field is generated using a conditional diffusion model. Simultaneously, an analytical function is used to parametrically model the target trend field. Then, modulation coefficients are determined, and the target trend field and the simulated stationary texture field are amplitude-modulated and spatially reconstructed. Finally, the optimal trend control parameters are derived inversely based on a constrained genetic algorithm to generate the final non-stationary corrosion pipeline random field. This invention solves the problem of existing technologies being unable to simulate corrosion non-stationarity through the decoupling and reconstruction of trend and texture, providing an accurate data foundation for pipeline structural integrity assessment.

Description

Technical Field

[0001] This invention relates to the field of steel pipe corrosion morphology modeling, specifically to a method for generating random fields for non-stationary corrosion pipelines through trend texture reconstruction. Background Technology

[0002] Corrosion of in-service oil and gas pipelines is a complex stochastic process, and its surface morphology directly determines the stress distribution and residual strength of the structure. To accurately assess the structural integrity of pipelines, high-fidelity digital characterization of corrosion morphology is necessary. Early methods simplified corrosion pits into regular geometric shapes; this oversimplification fails to capture the random fluctuations of the actual corrosion surface, leading to significant uncertainty in safety assessment results.

[0003] To address this issue, modeling methods based on random field theory have emerged. These methods can generate corrosion surfaces with a realistic microscopic appearance by learning the statistical properties of real corrosion samples, such as autocorrelation functions or power spectral density. However, almost all current random field modeling techniques, including some published patents, are based on a key assumption that often contradicts engineering realities: the corrosion process is spatially uniform and stationary. This implies that the generated corrosion field possesses the same statistical characteristics, such as mean and variance, at any location.

[0004] In fact, due to factors such as the varying effectiveness of pipeline contact with the external environment under gravity and local temperature and humidity changes, pipeline corrosion often exhibits significant non-stationarity. For example, in some service environments, corrosion at the bottom of the pipeline is often much more severe than at the top, forming a macroscopically identifiable corrosion trend. Existing technologies model this macroscopic, gradually changing corrosion trend together with microscopic, purely random corrosion textures, resulting in models that cannot independently control the distribution pattern of macroscopic corrosion or reproduce non-stationary characteristics. Consequently, the generated corrosion field is severely deviated from actual operating conditions. Summary of the Invention

[0005] Based on the above-mentioned technical problems, this invention proposes a method for generating random fields for non-stationary corrosion pipelines through trend texture reconstruction.

[0006] The technical solution adopted in this invention is:

[0007] A method for generating a random field for trend texture reconstruction of a non-stationary corroded pipeline includes the following steps:

[0008] Step S1: Scan and unfold the real corroded pipeline, and filter out the macroscopic shape error of the real corroded pipeline by ultra-low frequency filtering to obtain the pure corrosion height field;

[0009] Step S2: Apply a low-to-medium frequency filter to the pure corrosion height field obtained in step S1 to decompose it into a non-stationary trend field describing the macroscopic distribution of corrosion and a residual field representing local random fluctuations.

[0010] Step S3: Calculate the local fluctuation amplitude of the residual field obtained in step S2 at each point in space, and use the local fluctuation amplitude to normalize the residual field obtained in step S2 point by point to obtain a normalized stable texture field.

[0011] Step S4: Calculate the roughness parameters and corresponding power spectral density of the normalized stationary texture field obtained in step S3, and establish a mapping relationship database between roughness parameters and power spectral density.

[0012] Step S5: Based on the mapping relationship database of roughness parameters and power spectral density obtained in step S4, train the conditional diffusion model; input the target roughness parameters into the trained conditional diffusion model to generate the corresponding power spectral density; then, use a random harmonic function to inversely transform the generated power spectral density into a simulated stationary texture field.

[0013] Step S6: Establish an analytical function containing trend control parameters to represent the target non-stationary trend field;

[0014] Step S7: Based on the non-stationary trend field obtained in step S2 and the local fluctuation amplitude calculated in step S3, perform statistical regression analysis to determine the modulation coefficient that correlates the macroscopic corrosion depth with the microscopic fluctuation amplitude.

[0015] Step S8: Use the target non-stationary trend field generated in step S6 as a reference, and use it together with the modulation coefficient obtained in step S7 to perform amplitude modulation on the stationary texture field simulated in step S5, and initially reconstruct the erosion field.

[0016] Step S9: Based on the initial reconstruction of the corrosion field in Step S8, a closed-loop optimization problem is constructed and solved using a constrained genetic algorithm. The trend control parameters are then derived in reverse, thereby generating the final non-stationary corrosion random field.

[0017] The beneficial technical effects of the present invention are as follows:

[0018] This invention creatively decomposes corrosion morphology into a macroscopic non-stationary trend field and a microscopic stationary texture field, and establishes a spatial modulation reconstruction and closed-loop optimization mechanism between the two, fundamentally solving the problem that existing technologies cannot simulate the non-stationarity of corrosion. This invention constructs a fully digitalized process from data decoupling to independent generation and then to accurate reconstruction, achieving high-fidelity simulation of environmentally relevant, parameter-controllable corrosion random fields that combine macroscopic deterministic trends with microscopic randomness. This provides a high-fidelity data foundation for refined safety assessment of pipeline structures and digital twin applications.

[0019] Specifically, the present invention has the following advantages:

[0020] (1) This invention proposes and implements the “trend-texture decoupling” modeling paradigm for corrosion fields, which can accurately reproduce complex non-stationary corrosion morphologies with clear macroscopic distribution characteristics, such as gravity pits and strip corrosion, greatly improving the physical realism of the simulation.

[0021] (2) By decoupling, this invention achieves independent parameterized control of macroscopic trends, such as corrosion depth, location, and range, as well as microscopic textures, such as roughness. This avoids the problem in traditional integrated modeling where adjusting some roughness affects other roughnesses, and significantly improves control accuracy and flexibility.

[0022] (3) In the process of applying macroscopic trends, the present invention constructs a global optimization mechanism that includes microscopic statistical feature constraints, ensuring that while introducing non-stationary trends, the microscopic texture statistical characteristics of the reconstructed field are still strictly anchored to the feature space learned from real data, thereby ensuring the full-scale physical consistency of the generated field in macroscopic distribution and microscopic texture. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for generating a non-stationary corrosive pipeline random field for trend texture reconstruction according to the present invention;

[0024] Figure 2 The diagram shows the original, real corroded pipeline involved in the embodiments of the present invention; where (a) is the original view; and (b) is the ideal unfolded view of the original corroded pipeline.

[0025] Figure 3 This is a three-scale separation diagram of pipeline corrosion involved in the embodiments of the present invention; wherein (a) is the surface height of manufacturing error removed by ultra-low frequency filtering; (b) is the macroscopic corrosion trend diagram obtained by medium and low frequency filtering; and (c) is the pure stable texture field diagram obtained by subtracting the first two from the original surface.

[0026] Figure 4 This is a power spectral density (PSD) diagram of the microscopic stationary texture field involved in the embodiments of the present invention;

[0027] Figure 5 This is a diagram of the U-Net network architecture of the conditional diffusion model involved in the embodiments of the present invention;

[0028] Figure 6 The images show a comparison between the PSD of the corroded surface generated by the conditional diffusion model involved in the embodiments of the present invention and the real PSD; where (a) is the real PSD image and (b) is the simulated PSD image.

[0029] Figure 7This is a schematic diagram illustrating the reconstruction process of corrosion field trends and textures involved in the embodiments of the present invention;

[0030] Figure 8 This is a flowchart of the constrained genetic optimization algorithm involved in the embodiments of the present invention;

[0031] Figure 9 This is a schematic diagram of the final non-stationary corrosion field generated in an embodiment of the present invention. Detailed Implementation

[0032] This invention discloses a method for generating a random field for non-stationary corrosion pipelines through trend texture reconstruction. This method decouples the trend and texture, generates them independently, and then reconstructs them to obtain a random field for non-stationary corrosion pipelines. Specifically, it decouples the macroscopic corrosion trend from the microscopic corrosion texture and independently controls and reconstructs both with high fidelity to obtain the random field. The core idea of ​​this invention lies in the profound understanding that the real corrosion morphology is composed of two components with different properties: one is the non-stationary trend that determines how corrosion is distributed and changes gradually at the macroscopic scale; the other is the statistically uniform stationary texture that determines how corrosion fluctuates randomly at the microscopic scale. This invention innovatively proposes to decouple these two components and establishes a complete technical process of data analysis, independent generation, parameter control, and optimized reconstruction, achieving high-fidelity and high-flexibility simulation of non-stationary corrosion fields. This method can not only generate corrosion surfaces with realistic microscopic roughness but also accurately reproduce macroscopic corrosion patterns caused by environmental factors, such as accelerated corrosion at the bottom of pipelines, thus providing a more realistic data foundation for subsequent engineering analysis.

[0033] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0034] like Figure 1 As shown, a method for generating a random field for trend texture reconstruction of a non-stationary corroded pipeline specifically includes the following steps:

[0035] S1. A non-contact 3D laser scanner is used to perform high-precision scanning of the outer surface of multiple real corroded pipes, acquiring their 3D spatial coordinate point cloud data. The point cloud data is then idealized and unfolded. The central axis and average radius of the pipe are fitted using the least squares method. All point cloud data are projected onto an ideal cylindrical surface centered on this axis and with the average radius as its radius. This is then unfolded along the axial and circumferential directions to form a two-dimensional rectangular height field data matrix. The original pipe shape and the idealized unfolded shape are shown below. Figure 2As shown. Subsequently, a two-dimensional ultra-low frequency Gaussian filter is applied to the unfolded height field, with a cutoff wavelength of approximately 1 / 5 to 1 / 2 of the pipe circumference, to filter out macroscopic shape errors caused by the manufacturing process of each pipe. These errors mainly originate from geometric deviations during pipe production, typically around one-thousandth of the pipe dimension. A smooth surface representing the pipe manufacturing error profile is obtained, as shown. Figure 3 As shown in (a), subtracting the manufacturing error profile from the original unfolded height field yields a pure corrosion height field containing only corrosion information and no geometric deviations. .

[0036] S2, the pure corrosion height field obtained in step S1 A two-dimensional, low-to-mid-frequency Gaussian filter is applied. The cutoff wavelength of this filter is chosen to be much larger than the average size of a single corrosion pit, but smaller than the pipe circumference, to extract the macroscopic non-stationary trend determined by both the service environment and the degree of corrosion. The result after filtering is the macroscopic non-stationary trend field. ,like Figure 3 As shown in (b), the original pure corrosion height field is... Subtract the extracted macroscopic non-stationary trend field This yields the residual field representing local random fluctuations. The calculation formula is as follows:

[0037] (1)

[0038] In the formula, It is a pure corrosion high field; It is a non-stationary trend field; For the remaining field; These are the axial and circumferential coordinates of the pipeline, respectively.

[0039] S3, the remaining field obtained in step S2 The local standard deviation is calculated using a sliding window to obtain the local standard deviation field. This represents the local fluctuation amplitude of a non-stationary trend field. Subsequently, the remaining field is analyzed using the following formula. By performing point-by-point normalization, a normalized stationary texture field is calculated. ,like Figure 3 As shown in (c).

[0040] (2)

[0041] In the formula, To normalize the stable texture field; This represents the local standard deviation field.

[0042] The results obtained from the entire three-scale separation process include the manufacturing error surface, the macroscopic non-stationary trend field, and the purely stationary texture field, such as... Figure 3 As shown.

[0043] S4. Calculate the statistical characteristics of a large number of normalized, stationary texture field samples extracted from multiple real corroded pipes. For each size... Discrete normalized stationary texture field Sample, in which , , The number of points along the axial direction. To count the number of points along the circumferential direction, or in other words, the number of coordinate points along the axial and circumferential directions respectively, a set of four core roughness parameters and their power spectral density (PSD) is calculated, and these are paired to form a mapping database of roughness parameters and PSDs. The power spectral density is also often referred to as a two-dimensional power spectral density matrix, i.e., a two-dimensional PSD matrix.

[0044] First, calculate the four core roughness parameters. Root mean square height. The formula used to characterize the overall dispersion of surface height is as follows:

[0045] (3)

[0046] In the formula, The root mean square height, For the i-th data point in the axial direction, Let j be the j-th data point in the circumferential direction. Root mean square gradient. The formula used to characterize the local steepness or roughness of a surface is as follows:

[0047] (4)

[0048] Skewness The formula used to characterize the asymmetry of surface height distribution, i.e., the relative dominance of peaks and valleys, is as follows:

[0049] (5)

[0050] Kudo The formula used to characterize the sharpness or flatness of surface height distribution is as follows:

[0051] (6)

[0052] Next, the power spectral density of the surface is calculated. For normalized stable texture fields Performing a two-dimensional discrete Fourier transform yields its complex representation in the frequency domain. :

[0053] (7)

[0054] In the formula, , respectively, are the discrete wavenumbers along the axial direction (x) and the circumferential direction (y), where i is the imaginary unit. Power spectral density The result is calculated from the square of the magnitude of the Fourier transform:

[0055] (8)

[0056] In the formula, For wavenumber The power spectral density value at that location; These are the physical lengths of the surface in the axial (x) and circumferential (y) directions, respectively. For complex numbers The modulus. A typical power spectral density morphology of a microscopic stationary textured field is as follows: Figure 4 As shown.

[0057] Finally, the four roughness parameters calculated for each normalized stationary texture field sample are... , , , The vector formed and the corresponding power spectral density It is stored in the database as a data pair.

[0058] S5. Generate the target PSD using a conditional diffusion model. To achieve high-fidelity generation of the normalized stationary texture field, a PSD generation method based on a conditional diffusion model is adopted. First, a large number of data pairs are collected from the database established in step S4. Each data pair contains a four-dimensional roughness parameter vector and its corresponding real two-dimensional PSD matrix. The conditional diffusion model comprises two processes: forward diffusion and backward denoising. The forward diffusion process is defined as a parameterized Markov chain, where the total... Within each time step, it gradually evolves into an original two-dimensional PSD matrix. Gradually add Gaussian noise. At the... time step Noisy samples Generated by the following formula:

[0059] (9)

[0060] In the formula, This is the original two-dimensional PSD matrix; In time step A noisy two-dimensional PSD matrix; The cumulative noise figure, For time steps Noise scheduling parameters; To obtain from the standard normal distribution The noise in the sampled data.

[0061] The goal of the reverse denoising process is to reconstruct the original data from the noise, which is achieved by training a denoising neural network. This is achieved using noisy PSDs, or in other words, noisy samples. Current time step and the roughness parameter vector as a generation condition As input, its task is to predict what will be added during the forward process. Noise components in .

[0062] In this invention, the denoising network adopts a U-Net architecture, such as... Figure 5 As shown, the network consists of an encoder path and a decoder path. The encoder comprises multiple convolutional blocks, each containing a convolutional layer, a group normalization layer, and a SiLU activation function. It uses strided convolutions for downsampling, progressively extracting and compressing features. Simultaneously, time-step information... The vector is converted into a feature vector through a sinusoidal positional encoding layer, and then combined with the conditional vector, which serves as the roughness parameter vector for generation. Together, these features are injected into each encoder and decoder block through projection and addition operations. The decoder path is upsampled through transposed convolutions to progressively restore spatial resolution, and then concatenated with features of the corresponding scale in the encoder path through skip connections to preserve high-frequency details. The final output layer of the network is a convolutional layer whose output channel number is equal to the number of input noisy samples. The number of channels is the same. The training objective of the network is to minimize the difference between the predicted noise and the actual noise. A simplified mean squared error loss function is used:

[0063] (10)

[0064] In the formula, For simplified mean squared error loss; Expressing expectations; From The time step for uniform sampling in the middle; This is a neural network model.

[0065] After model training is complete, the PSD generation stage begins. This is done when the user specifies a set of target roughness parameters. At that time, the generation process starts from a pure Gaussian noise sample. Start, Iteration The noise is denoised in one step to generate the target PSD matrix. Its comparison with the PSD of the real sample is as follows: Figure 6 As shown.

[0066] Subsequently, the generated target PSD matrix is ​​processed using a second-type stochastic harmonic function (SHF-II). The inverse transform is used to obtain a normalized stationary texture field in the spatial domain, i.e., to simulate a stationary texture field. The calculation formula is as follows:

[0067] (11)

[0068] In the formula, To generate a simulated smooth texture field; These represent the number of discrete frequency components in the x and y directions, respectively. and Let m and n be the discrete wavenumber components corresponding to the summation indices m and n in the x and y directions, respectively, and be defined as follows: and ; and In order to be in Random phase angles that are independently and uniformly distributed over an interval; This is the amplitude coefficient.

[0069] Amplitude coefficient The calculation formula is:

[0070] (12)

[0071] In the formula, For wavenumber The power spectral density value at that location; and For wavenumber increments, respectively defined as and ; These are the physical lengths of the surface in the axial (x) and circumferential (y) directions, respectively.

[0072] S6. Establish an analytical function containing physical parameters, or trend control parameters, to represent and control the target non-stationary trend field. (This involves defining the target non-stationary trend field.) This can be represented as an analytic function. Since buried pipelines are typically placed horizontally along their axial direction, their corrosion tendency usually remains constant along the axial direction but varies significantly along the circumferential direction. Therefore... It can be seen as The function can Equivalent to For the circumferential direction The uneven corrosion trend is represented by the Sigmoid function:

[0073] (13)

[0074] In the formula, For circumferential direction The target of the change is a non-stationary trend field; This represents the maximum depth of the corroded area. The steepness of the corrosion transition zone; This marks the starting point of the corrosion zone. The width of the corroded area; The background corrosion depth. Together they constitute the set of trend control parameters.

[0075] S7. The macroscopic trend field separated from the real corrosion data in steps S2 and S3. and the calculated local standard deviation field Perform linear regression analysis and fit the following linear model:

[0076] (14)

[0077] In the formula, Let be the modulation coefficient to be solved; The regression error is used. The optimal value is obtained by solving the least squares method. value.

[0078] S8. The macroscopic target non-stationary trend field defined in step S6. The microscopic simulated smooth texture field generated in step S5 Reconstruction is then performed. First, based on the modulation coefficients obtained in step S7... Calculate the local standard deviation modulation field associated with the target trend field. :

[0079] (15)

[0080] Subsequently, the two are synthesized into a non-stationary corrosion random field using formula (16). :

[0081] (16)

[0082] Substituting equation (15) into equation (16), we obtain the reconstructed formula:

[0083] (17)

[0084] In the formula, This is a preliminary non-stationary corrosion random field; The target is a non-stationary trend field; To simulate a smooth texture field; is the modulation coefficient.

[0085] The schematic process of deconstructing and spatially modulating the trend texture of the entire corrosion field is as follows: Figure 7 As shown.

[0086] S9. Construct a trend control parameter To optimize the closed-loop optimization problem, the objective is to make the macroscopic features of the generated non-stationary corrosion random field approximate the user-specified target while maintaining the constraint that the statistical properties of the micro-texture remain unchanged. The constrained genetic optimization algorithm flow is as follows: Figure 8 As shown. First, determine the trend control parameters to be optimized. And randomly generate several sets of parameters within the preset parameter value range as the initial population. Then enter the iterative optimization process, for each individual in the population, substitute its parameters into formula (13) to generate the corresponding non-stationary trend field, and combine it with the stationary texture field generated in step S8, and synthesize the current non-stationary corrosion field according to formula (17).

[0087] Then define a fitness function that includes the objective function and the penalty term. Used to evaluate each individual (i.e., each group of trend control parameters) The fitness function is calculated as follows: (The formula for calculating the fitness function is:)

[0088] (18)

[0089] In the formula, The objective function is... The penalty function. The objective function. The difference between the macroscopic statistical characteristics of the reconstructed field and the user-specified target characteristics is quantified to drive the simulation results to approximate the macroscopic target. The calculation formula is as follows:

[0090] (19)

[0091] In the formula, To optimize based on the current variables The final field generated The calculated macroscopic characteristic values, such as the ratio of the standard deviations of the upper and lower surfaces of the pipe; The target ratio specified by the user. Penalty function. Used to handle constraints and ensure that micro-texture properties are not destroyed during optimization, its calculation formula is as follows:

[0092] (20)

[0093] In the formula, The number of constraints; For the first The penalty factor for each constraint is a large positive number; For the first The constraint function is calculated using the following formula:

[0094] (twenty one)

[0095] In the formula, For the first One roughness parameter, The tolerance is set to a preset value. A penalty function is used to check whether the micro-roughness of the reconstructed field meets the constraints. Individuals exceeding the tolerance range are penalized to ensure the fidelity of the micro-texture. Based on this, the next generation population is generated through genetic operations such as roulette wheel selection, arithmetic crossover, and non-uniform mutation, and the above field reconstruction and fitness evaluation process is repeated. Iteration stops when the preset maximum number of iterations is reached or the fitness function converges, and the individual with the lowest fitness is output as the optimal trend control parameter. The specific morphology of a final non-stationary corrosion field with obvious bottom corrosion intensification characteristics generated by this method is shown below. Figure 9 As shown.

[0096] This invention, through the aforementioned steps, constructs a complete technical chain from measured data analysis to trend and texture decoupling, and then to parameterized independent generation and optimized reconstruction, achieving high-fidelity, rapid, and controllable generation of corroded pipeline morphologies with arbitrary non-stationary characteristics. This method overcomes the fundamental deficiency of traditional random field models in simulating corrosion non-stationarity, and ensures the independence and accuracy of macroscopic trend and microscopic texture control through a decoupling framework. It provides a high-fidelity morphology data foundation for refined finite element analysis of pipeline structures, remaining life prediction, and digital twin operation and maintenance, demonstrating significant engineering application value in ensuring the safety of energy infrastructure.

[0097] For any parts not mentioned in the above embodiments, existing technologies can be adopted or referenced.

[0098] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the above embodiments. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should be protected by the present invention.

Claims

1. A method for generating random fields for non-stationary corrosion pipelines through trend texture reconstruction, characterized in that... Includes the following steps: Step S1: Scan and unfold the real corroded pipeline, and filter out the macroscopic shape error of the real corroded pipeline by ultra-low frequency filtering to obtain the pure corrosion height field; Step S2: Apply a low-to-medium frequency filter to the pure corrosion height field obtained in step S1 to decompose it into a non-stationary trend field describing the macroscopic distribution of corrosion and a residual field representing local random fluctuations. Step S3: Calculate the local fluctuation amplitude of the residual field obtained in step S2 at each point in space, and use the local fluctuation amplitude to normalize the residual field obtained in step S2 point by point to obtain a normalized stable texture field. Step S4: Calculate the roughness parameters and corresponding power spectral density of the normalized stationary texture field obtained in step S3, and establish a mapping relationship database between roughness parameters and power spectral density. Step S5: Based on the mapping relationship database of roughness parameters and power spectral density obtained in step S4, train the conditional diffusion model; input the target roughness parameters into the trained conditional diffusion model to generate the corresponding power spectral density; then, use a random harmonic function to inversely transform the generated power spectral density into a simulated stationary texture field. Step S6: Establish an analytical function containing trend control parameters to represent the target non-stationary trend field; Step S7: Based on the non-stationary trend field obtained in step S2 and the local fluctuation amplitude calculated in step S3, perform statistical regression analysis to determine the modulation coefficient that correlates the macroscopic corrosion depth with the microscopic fluctuation amplitude. Step S8: Use the target non-stationary trend field generated in step S6 as a reference, and use it together with the modulation coefficient obtained in step S7 to perform amplitude modulation on the stationary texture field simulated in step S5, and initially reconstruct the erosion field. Step S9: Based on the initial reconstruction of the corrosion field in Step S8, a closed-loop optimization problem is constructed and solved using a constrained genetic algorithm. The trend control parameters are then derived in reverse, thereby generating the final non-stationary corrosion random field.

2. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 1, characterized in that, In step S1: A non-contact 3D laser scanner is used to scan the outer surface of multiple real corroded pipes to obtain their 3D spatial coordinate point cloud data; the point cloud data is idealized and unfolded, and the central axis and average radius of the pipe are fitted by the least squares method. All point cloud data are projected onto an ideal cylindrical surface with the central axis as the center and the average radius as the radius, and unfolded along the axial and circumferential directions to form a two-dimensional rectangular height field. Subsequently, a two-dimensional ultra-low frequency Gaussian filter is applied to the two-dimensional rectangular height field to filter out macroscopic shape errors caused by the manufacturing process of each real corroded pipe, thus obtaining the pure corrosion height field. , These are the axial and circumferential coordinates of the pipeline, respectively.

3. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 2, characterized in that, In step S2: the pure corrosion height field obtained in step S1 Applying a two-dimensional low-frequency Gaussian filter, the filtered result is a non-stationary trend field describing the macroscopic distribution of corrosion. ; to pure corrosion high field Subtract non-stationary trend fields This yields the residual field representing local random fluctuations. The calculation formula is: (1) In the formula, It is a pure corrosion high field; It is a non-stationary trend field; For the remaining field.

4. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 3, characterized in that, In step S3: the residual field obtained in step S2 The local standard deviation is calculated using a sliding window to obtain the local standard deviation field. This represents the local fluctuation amplitude of a non-stationary trend field; Subsequently, the remaining fields By performing point-by-point normalization, a normalized stationary texture field is calculated. The calculation formula is: (2) In the formula, To normalize the stable texture field; This represents the local standard deviation field.

5. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 4, characterized in that, In step S4: Calculate the statistical characteristics of multiple normalized stationary texture fields extracted from multiple real corroded pipes; For each dimension Normalized stable texture field ,in , , The number of points along the axial direction. To count the number of points along the circumferential direction, a set of four roughness parameters and their corresponding power spectral densities are calculated, and these are paired to form a database of the mapping relationship between roughness parameters and power spectral densities. First, calculate four roughness parameters: root mean square height, root mean square gradient, skewness, and kurtosis. Root mean square height The formula used to characterize the overall dispersion of surface height is as follows: (3) In the formula, The root mean square height, For the i-th data point in the axial direction, This represents the j-th data point in the circumferential direction. Root mean square gradient The formula used to characterize the local steepness of a surface is as follows: (4) Skewness The formula used to characterize the asymmetry of surface height distribution is as follows: (5) Kudo The formula used to characterize the sharpness or flatness of surface height distribution is as follows: (6) Next, the power spectral density is calculated. ; for normalized stable texture fields Performing a two-dimensional discrete Fourier transform yields its complex representation in the frequency domain. : (7) In the formula, , i, and y, respectively, represent the discrete wavenumbers along the axial direction (x) and the circumferential direction (y), where i is the imaginary unit; power spectral density. The result is calculated from the square of the magnitude of the Fourier transform: (8) In the formula, For wavenumber The power spectral density value at that location; These are the physical lengths of the surface in the axial (x) and circumferential (y) directions, respectively. For complex numbers The model; Finally, the four roughness parameters calculated for each normalized stationary texture field are... , , , The vector formed and the corresponding power spectral density It is stored in the database as a data pair.

6. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 5, characterized in that, In step S5: the conditional diffusion model includes two processes: forward diffusion and reverse denoising; the forward diffusion process is defined as a parameterized Markov chain, in total... Within each time step, it gradually moves towards an original power spectral density. Add Gaussian noise, in the first Each time step, noisy samples Generated by the following formula: (9) In the formula, This represents the original power spectral density; In time step The noisy power spectral density; The cumulative noise figure, For time step Noise scheduling parameters; To obtain from the standard normal distribution Noise in the mid-sample; The reverse denoising process reconstructs the original data from the noise by training a denoising neural network. To achieve this; the denoising neural network uses noisy samples Current time step and the roughness parameter vector as a generation condition As input, its task is to predict the addition of noisy samples during the forward pass. Noise in This denoising neural network uses the U-Net architecture, and its output channel count is equal to that of the noisy samples. The number of channels is the same; a simplified mean square error loss function is used: (10) In the formula, The simplified mean squared error loss function; Expressing expectations; From The time step for uniform sampling in the middle; It is a neural network model; After the model training is completed, the power spectral density generation stage begins; when a set of target roughness parameters is specified... At that time, the generation process starts from a pure Gaussian noise sample. Start, Iteration The noise is denoised in one step to generate the target power spectral density. ; Subsequently, the generated target power spectral density is obtained using a second-type stochastic harmonic function. Inverse transformation to simulated stationary texture field The calculation formula is: (11) In the formula, For simulating a smooth texture field; These represent the number of discrete frequency components in the x and y directions, respectively. and Let m and n be the discrete wavenumber components corresponding to the summation indices m and n in the x and y directions, respectively, and be defined as follows: and ; and In order to be in Random phase angles that are independently and uniformly distributed over an interval; The amplitude coefficient; Amplitude coefficient The calculation formula is: (12) In the formula, For wavenumber Target power spectral density at; and For wavenumber increments, respectively defined as and .

7. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 6, characterized in that, In step S6: the target non-stationary trend field Represented as an analytical function, since buried pipelines are placed horizontally along the axial direction, their corrosion tendency remains constant along the axial direction but varies along the circumferential direction. See as The function will Equivalent to For the circumferential direction The uneven corrosion trend is represented by the Sigmoid function: (13) In the formula, For circumferential direction The target of the change is a non-stationary trend field; This represents the maximum depth of the corroded area. The steepness of the corrosion transition zone; This marks the starting point of the corrosion zone. The width of the corroded area; Background corrosion depth; Together they constitute the set of trend control parameters.

8. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 7, characterized in that, In step S7: the non-stationary trend field in step S2 and the local standard deviation field calculated in step S3 Perform linear regression analysis and fit the following linear model: (14) In the formula, The modulation coefficient; The regression error is used; the optimal value is obtained by solving the least squares method. value.

9. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 8, characterized in that, In step S8: the target non-stationary trend field obtained in step S6 is... The simulated smooth texture field obtained in step S5 Refactor; First, based on the modulation coefficients obtained in step S7 Calculate the local standard deviation modulation field associated with the target non-stationary trend field. : (15) Subsequently, a non-stationary corrosion random field is synthesized using formula (16). : (16) Substituting equation (15) into equation (16), we obtain the reconstructed formula: (17) In the formula, This is a synthesized non-stationary corrosion random field; The target is a non-stationary trend field; For simulating a smooth texture field; is the modulation coefficient.

10. The method for generating a non-stationary corrosion pipeline random field for trend texture reconstruction according to claim 9, characterized in that, In step S9: Construct a trend control parameter To optimize the closed-loop optimization problem of variables, the objective of this optimization problem is to make the macroscopic characteristics of the generated non-stationary corrosion random field approximate the set target while satisfying the constraint that the statistical properties of micro-texture remain unchanged. The steps of the constrained genetic optimization algorithm are as follows: First, determine the trend control parameters to be optimized. And randomly generate several sets of parameters within the preset parameter value range as the initial population; Then, the iterative optimization process is entered. For each individual in the population, its parameters are substituted into formula (13) to generate the corresponding target non-stationary trend field. Combined with the stationary texture field generated in step S8, the current non-stationary erosion random field is synthesized according to formula (17). Then define a fitness function that includes the objective function and the penalty term. Used to evaluate each group of trend control parameters The degree of superiority or inferiority; the formula for calculating the fitness function is: (18) In the formula, The objective function is... The penalty function; the objective function Its calculation formula is: (19) In the formula, To generate the final field based on the current optimization variables The calculated macroscopic characteristic values; The target ratio is set; penalty function The calculation formula is: (20) In the formula, The number of constraints; For the first A penalty factor for each constraint; For the first The constraint function is calculated using the following formula: (21) In the formula, For the first One roughness parameter, This is the preset tolerance; The next generation population is then generated through genetic operations, and the above reconstruction and fitness evaluation process is repeated. The iteration stops when the preset maximum number of iterations is reached or the fitness function converges, and the individual with the lowest fitness is output as the optimal trend control parameter.

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