Pipeline modeling method and device based on fractional Brownian motion

Abstract

The present invention provides a pipeline modeling method based on fractional Brownian motion. The method comprises the following steps: setting initial fracture surface parameters, wherein the initial fracture surface parameters include initial coordinates of four corner points and the value of the z-axis obeys a first Gaussian distribution; step S2, performing a first linear interpolation on the initial coordinates of the four corner points to obtain the midpoint coordinates and the center point coordinates of the four sides of the initial fracture surface, and updating the first Gaussian distribution at the same time; step S3, taking step S2 as a basic recursive process, performing n-1 linear interpolation on the initial fracture surface to generate a (2n+1) node number. 2 , size is 2 n ×2 n The target fracture surface is obtained and the first Gaussian distribution is updated; step S4, the fractal dimension is determined according to the Hurst index, and the fractal dimension and the target fracture surface are input into a preset modeling algorithm to generate a three-dimensional pipeline model, which can effectively complete the pipeline modeling and improve the accuracy of pipeline modeling.

Description

Technical Field

[0001] The present invention relates to the technical field of pipeline analysis, and in particular to a pipeline modeling method and device based on fractional Brownian motion. Background Art

[0002] Analytical testing of pipelines is one of the main methods for studying the engineering characteristics of pipelines. In actual operation, due to the complexity of the actual situation of pipelines, it is difficult and costly to directly use original pipelines for testing, and the cost performance is low. There are some methods in the prior art that use computer modeling to obtain pipeline roughness models, but these methods have heavy traces of artificial generation of the models, and are quite different from the real original pipelines in randomness. Therefore, the results obtained from experiments based on existing modeling methods are often not accurate enough. Summary of the invention

[0003] The purpose of the present invention is to provide a pipeline modeling method based on fractional Brownian motion, which can effectively complete pipeline modeling and improve the accuracy of pipeline modeling.

[0004] To achieve the above object, the present invention provides a pipeline modeling method based on fractional Brownian motion, comprising the following steps:

[0005] Step S1, setting the initial fracture surface parameters, the initial fracture surface parameters include the coordinates of the nodes at the four corners of the fracture surface and the first Gaussian distribution that the Z axis corresponding to the initial fracture surface must obey, the first Gaussian distribution has a mean of zero and a variance of σ 2 Gaussian distribution M(0,σ 2 );

[0006] Step S2: Perform the first linear interpolation on the coordinates of the nodes at the four corners of the fracture surface to obtain the midpoint coordinates and center coordinates of the four sides of the initial fracture surface, and update the first Gaussian distribution to have a mean of zero and a variance of Gaussian distribution in Calculated based on the preset Hurst index and the preset update formula;

[0007] Step S3: Using step S2 as the basic recursive process, perform n-1 linear interpolations on the initial fracture surface to generate a (2n+1) node number fracture surface. 2 , size is 2 n ×2 n The target fracture surface is updated with the first Gaussian distribution having a mean of zero and a variance of Gaussian distribution in Calculated according to the preset Hurst index and the preset update formula, n is a positive integer greater than 1;

[0008] Step S4: determine the fractal dimension according to the Hurst index, and input the fractal dimension and the target fracture surface into a preset modeling algorithm to generate a three-dimensional pipeline model.

[0009] Optionally, the preset update formula is:

[0010]

[0011] Where H is the Hurst index, which ranges from 0 to 1.

[0012] Optionally, the method for determining the fractal dimension according to the Hurst index is D=3-H, where D is the fractal dimension and H is the Hurst index.

[0013] Optionally, the pipeline modeling is completed in MATLAB software.

[0014] Beneficial effects of the invention: The invention provides a pipeline modeling method based on fractional Brownian motion, comprising the following steps: step S1, setting initial fracture surface parameters, the initial fracture surface parameters including the coordinates of the nodes at the four corners of the fracture surface and the first Gaussian distribution that the Z axis corresponding to the initial fracture surface must obey, the first Gaussian distribution being a Gaussian distribution M(0,σ2) with a mean of zero and a variance of σ2; step S2, performing a first linear interpolation on the coordinates of the nodes at the four corners of the fracture surface to obtain the midpoint coordinates and the center point coordinates of the four sides of the initial fracture surface, and updating the first Gaussian distribution to a Gaussian distribution with a mean of zero and a variance of σ2. Gaussian distribution in According to the preset Hurst index and the preset update formula; Step S3, taking step S2 as the basic recursive process, the initial fracture surface is further linearly interpolated n-1 times to generate a node number (2n+1) 2 , size is 2 n ×2 n The target fracture surface is updated with the first Gaussian distribution having a mean of zero and a variance of Gaussian distribution n is a positive integer greater than 1; step S4, determining the fractal dimension according to the Hurst index, and inputting the fractal dimension and the target fracture surface into a preset modeling algorithm to generate a three-dimensional pipeline model, which can effectively complete the pipeline modeling and improve the accuracy of pipeline modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to further understand the features and technical contents of the present invention, please refer to the following detailed description and drawings of the present invention. However, the drawings are only provided for reference and illustration and are not intended to limit the present invention.

[0016] In the accompanying drawings,

[0017] Figure 1 It is a schematic diagram of steps S1 to S3 of the pipeline modeling method based on fractional Brownian motion of the present invention;

[0018] Figure 2 It is a schematic diagram of step S4 of the pipeline modeling method based on fractional Brownian motion of the present invention;

[0019] Figure 3 The flowchart of the pipeline modeling method based on fractional Brownian motion of the present invention. DETAILED DESCRIPTION

[0020] To further illustrate the technical means and effects of the present invention, the following is a detailed description in conjunction with the preferred embodiments of the present invention and the accompanying drawings.

[0021] See also Figures 1 to 3 The present invention provides a pipeline modeling method based on fractional Brownian motion, comprising the following steps:

[0022] Step S1, setting the initial fracture surface parameters, the initial fracture surface parameters include the coordinates of the nodes at the four corners of the fracture surface and the first Gaussian distribution that the Z coordinate corresponding to the initial fracture surface must obey, the first Gaussian distribution has a mean of zero and a variance of σ 2 Gaussian distribution M(0,σ 2 ).

[0023] Specifically, combined Figure 1 In some embodiments of the present invention, step S1 specifically includes: assuming that the construction area of ​​the initial fracture surface is determined by the coordinates A0, B0, C0 and D0 of the nodes at the four corners of the fracture surface, and the value of the Z coordinate obeys N(0,σ2), where N(0,σ2) represents a Gaussian distribution with a mean of zero and a variance of σ2.

[0024] It should be noted that the initial fracture surface parameters are set in a preset three-dimensional coordinate system, wherein the coordinates of the nodes at the four corners of the fracture surface are represented by X-coordinates and Y-coordinates, and the Z-coordinate obeys the first Gaussian distribution mentioned above.

[0025] Step S2: Perform the first linear interpolation on the coordinates of the nodes at the four corners of the fracture surface to obtain the midpoint coordinates and center coordinates of the four sides of the initial fracture surface, and update the first Gaussian distribution to have a mean of zero and a variance of Gaussian distribution in Calculated based on the preset Hurst index and the preset update formula.

[0026] Step S3: Using step S2 as the basic recursive process, perform n-1 linear interpolations on the initial fracture surface to generate a (2n+1) node number fracture surface. 2 , size is 2n ×2 n The target fracture surface is updated with the first Gaussian distribution having a mean of zero and a variance of Gaussian distribution in Calculated according to the preset Hurst index and the preset update formula, n is a positive integer greater than 1;

[0027] Specifically, combined Figure 1 In some embodiments of the present invention, the processing of steps S2 to S3 includes:

[0028] like Figure 1 As shown, by averaging the coordinates of the nodes at the four corners of the fracture surface and the coordinates of the adjacent nodes, a central point A1 and four midpoints of each side B1, C1, D1 and E1 are linearly interpolated, and then Add variance to The random values ​​are as follows:

[0029]

[0030] Where H is the Hurst index, which ranges from 0 to 1.

[0031] Using the above steps as a basic recursive process, such as Figure 2 The values ​​of A2, B2, C2, D2, and E2 are interpolated as shown in Add variance to The random values ​​for are as follows:

[0032]

[0033] Repeat the above process and After each linear interpolation, a node number (2n+1) is generated. 2 , size is 2 n ×2 n The target fracture surface is It can be expressed as:

[0034]

[0035] That is, the preset update formula is:

[0036]

[0037] Where H is the Hurst index, which ranges from 0 to 1.

[0038] Preferably, in some embodiments of the present invention H is equal to 0.1.

[0039] Step S4: determine the fractal dimension according to the Hurst index, and input the fractal dimension and the target fracture surface into a preset modeling algorithm to generate a three-dimensional pipeline model.

[0040] Specifically, combined Figure 2 As shown in the figure, fractal dimension D is an important parameter to describe the roughness of fracture surface. Fractal characteristics can be used to reflect its complexity and irregularity. Generally speaking, the larger the fractal dimension D, the rougher the fracture surface. Previous studies have shown that fractal dimension D and Hurst index H can be written as the equation D = 3-H, which is used to construct three-dimensional graphics.

[0041] Finally, in some embodiments of the present invention, the raw data of the rough surface can be first generated by the MATLAB programming method, and then the parametric surface tool is used to perform surface lofting based on fBm called by the finite element analysis software COMSOL. By adjusting the maximum number of nodes and the relative tolerance, the relative error between the parametric coordinates and the actual coordinates is reduced, and the accuracy of the parameterization is improved. Finally, the rough surface of a pipeline with a length of 15m and a diameter of 1.2m is simulated, with a Hurst index of 0.1 and a fractal dimension D of 2.9.

[0042] As described above, for ordinary technicians in this field, various other corresponding changes and modifications can be made based on the technical solutions and technical concepts of the present invention, and all these changes and modifications should fall within the protection scope of the claims of the present invention.

Claims

1. A pipeline modeling method based on fractional Brownian motion, characterized in that: The steps include: Step S1, setting the initial fracture surface parameters, the initial fracture surface parameters include the coordinates of the nodes at the four corners of the fracture surface and the first Gaussian distribution that the Z axis corresponding to the initial fracture surface must obey, the first Gaussian distribution has a mean of zero and a variance of σ 2 Gaussian distribution M(0,σ 2 ); Step S2: Perform the first linear interpolation on the coordinates of the nodes at the four corners of the fracture surface to obtain the midpoint coordinates and center coordinates of the four sides of the initial fracture surface, and update the first Gaussian distribution to have a mean of zero and a variance of Gaussian distribution in Calculated based on the preset Hurst index and the preset update formula; Step S3: Using step S2 as the basic recursive process, perform n-1 linear interpolations on the initial fracture surface to generate a (2n+1) node number fracture surface. 2 , size is 2 n ×2 n The target fracture surface is updated with the first Gaussian distribution having a mean of zero and a variance of Gaussian distribution in Calculated according to the preset Hurst index and the preset update formula, n is a positive integer greater than 1; Step S4: determine the fractal dimension according to the Hurst index, and input the fractal dimension and the target fracture surface into a preset modeling algorithm to generate a three-dimensional pipeline model.

2. The pipeline modeling method based on fractional Brownian motion according to claim 1, characterized in that: The preset update formula is: Where H is the Hurst index, which ranges from 0 to 1.

3. The pipeline modeling method based on fractional Brownian motion according to claim 1, characterized in that: The method for determining the fractal dimension based on the Hurst index is D=3-H, where D is the fractal dimension and H is the Hurst index.

4. The pipeline modeling method based on fractional Brownian motion according to claim 1, characterized in that: The pipeline modeling was completed in MATLAB software.

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