A multi-scale tandem pipe erosion analysis method, system, and terminal.

Abstract

This invention belongs to the field of pipeline erosion prediction and evaluation technology, and relates to a multi-scale tandem bend erosion analysis method, system, and terminal. The analysis method includes: obtaining n sets of initial data based on the Latin hypercube sampling method; configuring simulation experiments to obtain n sets of simulation data based on the n sets of initial data; selecting a machine learning model and optimizing the hyperparameters of the machine learning model using a grid search method; training the machine learning model based on the simulation data to obtain a hyperparameter-optimized machine learning prediction model; predicting the erosion rate of the tandem bend based on the hyperparameter-optimized machine learning prediction model; and conducting multi-scale analysis of the factors and their influence on the erosion rate of the tandem bend to obtain the analysis results. This invention explains the intrinsic relationship between the model's erosion rate prediction and the prediction of gas-solid erosion in the tandem bend through SHAP analysis, response surface analysis, and Stokes equation analysis, increasing the real-time prediction capability and interpretability of industrial pipeline erosion.

Description

Technical Field

[0001] This invention relates to the field of pipeline erosion prediction and evaluation technology, and in particular to a multi-scale tandem bend erosion analysis method, system and terminal. Background Technology

[0002] In recent years, pipeline and equipment damage accidents caused by erosion have been on the rise. During the extraction of crude oil and natural gas from reservoirs, these fluids often carry sand and other impurity particles. Under high flow velocities, these particles violently impact the pipeline walls, leading to erosion and potentially causing malfunctions in critical equipment within the oil and gas industry, ultimately resulting in a complete shutdown of the entire production system. It is noteworthy that sand particles, possessing kinetic energy, exhibit particularly significant erosive effects in areas where fluid dynamics change drastically (e.g., at geometries with rapidly changing flow velocities or under specific flow conditions). Therefore, accurately predicting erosion and controlling it within acceptable limits to ensure production continuity is crucial for oil and gas companies. It not only saves economic costs but also effectively prevents the leakage of other compounds from pipelines, thus avoiding environmental damage. However, predicting erosion in sand-laden single-phase and multiphase flows is extremely complex because the process involves numerous interacting parameters that collectively determine the degree of particle erosion of the pipeline walls. Solid particle erosion has been extensively studied in the early stages, and scholars have developed empirical prediction models for different flow conditions. However, most of these empirical prediction models are based on fitting experimental data to obtain empirical equations for erosion, which still differ significantly from the actual erosion situation.

[0003] Currently, some scholars are still promoting research on empirical prediction models, but these typically use simplified models of multiphase flow to calculate local velocities of the phases and determine the impact velocities of sand particles. Therefore, the accuracy of erosion prediction in multiphase flow is limited only by the accuracy of the multiphase flow model. Furthermore, due to limitations in experimental conditions and numerous influencing factors, most tests can only examine the maximum erosion rate across the entire elbow or the linear erosion morphology around the elbow, making it difficult to obtain the influence of various factors on the erosion phenomenon. Currently, the mainstream research method for elbow erosion problems is Computational Fluid Dynamics (CFD). Based on the flexibility and efficiency of CFD, numerous studies have emerged on particle trajectories, erosion morphologies, and elbow erosion distribution under different influencing factors. However, multiphase flow in pipelines presents a complex fluid environment. Accurate flow field simulation using CFD methods under complex pipeline structures and turbulent conditions requires significant computational resources and time, which is detrimental to real-time analysis and optimization. With continuous exploration in the field of computer science, artificial intelligence has been widely applied in numerous engineering applications. Some researchers have applied machine learning methods from artificial intelligence to erosion prediction, attempting to build corresponding erosion prediction models from a data-driven perspective. Even though artificial intelligence models perform well in processing complex data and providing accurate predictions, their decision-making processes are often hidden or overly complex, making them difficult to interpret or explain.

[0004] In summary, although existing technologies have been used to predict and analyze pipeline erosion using empirical formulas, CFD simulation analysis, and artificial intelligence algorithms, accurate predictions are often impossible when dealing with gas-dominated solid particle erosion in pipelines due to the complex internal flow states and erosion mechanisms. These predictions are mostly limited to the single effect of different factors on elbow erosion. For pipeline systems, tandem elbows exhibit even more complex flow states than single elbows, yet research on erosion prediction and analysis for tandem elbows is virtually nonexistent. Summary of the Invention

[0005] The purpose of this invention is to address the current situation where existing technologies struggle to accurately predict pipeline erosion caused by gas-dominated solid particles, and research on erosion prediction and analysis of tandem bends is almost nonexistent. This invention proposes a multi-scale tandem bend erosion analysis method, system, and terminal, which can predict the erosion rate of tandem bends with high accuracy, analyze the factors and their impact on the erosion rate of tandem bends at multiple scales, and provide engineering guidance for preventing tandem bend erosion.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a multi-scale cascaded pipe erosion analysis method, comprising the following steps:

[0008] S1. Obtain n sets of initial data based on the Latin hypercube sampling method;

[0009] S2. Configure the simulation experiment and obtain n sets of simulation data based on n sets of initial data;

[0010] S3. Select a machine learning model and optimize its hyperparameters using a grid search method;

[0011] S4. Train a machine learning model based on simulation data to obtain a hyperparameter-optimized machine learning prediction model;

[0012] S5. Predicting the erosion rate of series bends using a hyperparameter-optimized machine learning prediction model;

[0013] S6. Multi-scale analysis of the factors affecting the erosion rate of tandem bends and the degree of their influence, obtaining analytical results. Multi-scale analysis includes: SHAP analysis, response surface analysis, and Stokes equation analysis.

[0014] As one possible implementation method, the analysis results are as follows:

[0015]

[0016] in, This indicates the SHAP analysis results. This indicates the degree of influence of the interaction between any two factors. Effect(d0→pi) indicates the degree of influence of particle size on the upstream or downstream bend.

[0017] As one possible implementation, SHAP analysis can be performed using the following method:

[0018]

[0019] Where i∈{1,2}, p1 represents the upstream bend, and p2 represents the downstream bend. φ(M) represents the SHAP analysis result, which is the SHAP value calculation function based on the hyperparameter optimization machine learning prediction model. D represents the bend distance, R represents the bend curvature radius, V represents the bend inlet velocity, d0 represents the particle size, Q represents the total flow rate, j represents the j-th set of simulation data, 1≤j≤n, and n represents the n-th set of simulation data.

[0020] As one possible implementation, response surface analysis can be implemented using the following method:

[0021]

[0022] Where i∈{1,2}, p1 represents the upstream bend, p2 represents the downstream bend, x,y∈(D,R,V,d0,Q) and x≠y, D represents the bend distance, R represents the bend radius of curvature, V represents the bend inlet velocity, d0 represents the particle size, and Q represents the total flow rate. It represents the degree of influence of the interaction between any two factors; RSM stands for Response Surface Analysis.

[0023] As one possible implementation, the Stokes equations analysis is performed using the following method:

[0024]

[0025] Where, ρ p d represents particle density. p Let μ represent the particle diameter, u represent the fluid velocity, μ represent the fluid dynamic viscosity, and D represent the pipe diameter. The influence of particle size on upstream or downstream bends is as follows:

[0026]

[0027] Among them, Effect(d0→p1) represents the degree of influence of particle size on the upstream bend, and Effect(d0→p2) represents the degree of influence of particle size on the downstream bend.

[0028] As one possible implementation, the machine learning model is the CatBoost model, with hyperparameters including: learning rate, depth, and L2 regularization parameter; the hyperparameter optimization of the machine learning prediction model is as follows:

[0029] M = CatBoost[D Train ,θ * (a,b,c)]

[0030] Among them, D Train Let θ represent the training set in n sets of simulation data. * Let (a,b,c) represent the optimal parameters, and let (a,b,c) represent the CV parameter search space, where the CV parameters are k∈{1,2,3,4,5}.

[0031] As one possible implementation, S5 adopts the following method:

[0032]

[0033] in, The value represents the predicted erosion rate of the series bend, where D represents the bend distance, R represents the bend radius of curvature, V represents the bend inlet velocity, d0 represents the particle size, Q represents the total flow rate, and M represents the hyperparameter-optimized machine learning prediction model.

[0034] As one possible approach, simulation experiments include fluid flow modeling and particle trajectory tracking;

[0035] Fluid flow modeling includes: treating the gas as a continuous phase, using the Reynolds stress model as the turbulence model, and employing a reinforced wall treatment method for near-wall treatment;

[0036] Particle trajectory tracking is performed using the Lagrangian method, considering drag, gravity, and lift, but neglecting pressure gradient force and virtual mass force, and using the normal e-axis. n and tangential e t The wall recovery coefficient method is used to establish a springback model;

[0037] The Finnie erosion model was used as the erosion model.

[0038] Secondly, the present invention provides a multi-scale series bend corrosion analysis system, comprising:

[0039] The simulation data acquisition unit is used to acquire n sets of initial data based on the Latin hypercube sampling method, configure the simulation experiment, and obtain n sets of simulation data based on the n sets of initial data.

[0040] The hyperparameter-optimized machine learning prediction model acquisition unit is used to select a machine learning model, optimize the hyperparameters of the machine learning model based on the grid search method, train the machine learning model based on simulation data, and obtain the hyperparameter-optimized machine learning prediction model.

[0041] A series bend erosion rate prediction unit is used to predict the erosion rate of series bends based on a hyperparameter-optimized machine learning prediction model.

[0042] The erosion analysis unit for tandem bends is used for multi-scale analysis of the factors and their influence on the erosion rate of tandem bends, and to obtain analysis results. The multi-scale analysis includes: SHAP analysis, response surface analysis, and Stokes equation analysis.

[0043] Thirdly, the present invention provides a terminal including a processor and a communication interface coupled to the processor, the processor being used to run computer programs or instructions to implement a multi-scale series bend erosion analysis method provided in the first aspect.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] 1. The multi-scale erosion analysis method for series bends proposed in this invention predicts the erosion rate of series bends with high accuracy based on a hyperparameter-optimized machine learning prediction model. Through SHAP analysis, response surface analysis, and Stokes equation analysis, the intrinsic relationship between the model's erosion rate prediction and the prediction of gas-solid erosion in series bends can be further explained, increasing the real-time prediction capability and interpretability of industrial pipeline erosion data.

[0046] 2. The multi-scale erosion analysis method for series bends proposed in this invention analyzes the factors and their influence on the erosion rate of series bends from multiple perspectives. It uses SHAP analysis to quantify the importance of features (model-driven), response surface analysis to reveal the interaction (statistically driven), and Stokes equations to analyze the physical mechanism (physically driven), thus achieving a full-chain explanation from data to mechanism.

[0047] 3. The analytical conclusions obtained by using the multi-scale series bend erosion analysis method proposed in this invention can provide engineering guidance for preventing series bend erosion. For small particle conditions, the downstream bend structure needs to be optimized to alleviate secondary flow erosion; for large particle conditions, the impact resistance of the upstream bend material needs to be strengthened; for combined conditions, the flow rate and geometric parameters need to be balanced to reduce flow field turbulence.

[0048] 4. The multi-scale series bend erosion analysis method proposed in this invention can be extended to more complex pipeline systems (such as multi-bend and multiphase flow), providing a universal framework for industrial pipeline safety design. Attached Figure Description

[0049] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0050] Figure 1 This is a flowchart of a multi-scale series bend erosion analysis method in an embodiment of the present invention.

[0051] Figure 2 This is a schematic diagram showing the characteristic value distribution of 221 sets of operating parameters in an embodiment of the present invention;

[0052] Figure 3 This is a comparison of the prediction performance of various models on the average erosion rate of the wall of a series bend in the embodiments of the present invention.

[0053] Figure 4 This is a comparison of the prediction performance of various models for the maximum erosion rate of the upstream bend in the embodiments of the present invention.

[0054] Figure 5 This is a comparison of the prediction performance of various models for the maximum erosion rate of downstream bends in the embodiments of the present invention.

[0055] Figure 6 This is a visualization of the prediction of the average erosion rate of the wall of a series bend by the hyperparameter-optimized machine learning prediction model in an embodiment of the present invention.

[0056] Figure 7This is a visualization of the prediction of the maximum erosion rate of the upstream bend by the hyperparameter-optimized machine learning prediction model in an embodiment of the present invention.

[0057] Figure 8 This is a visualization of the prediction of the maximum erosion rate of the downstream bend by the hyperparameter-optimized machine learning prediction model in an embodiment of the present invention.

[0058] Figure 9 This invention provides the prediction and confidence interval of the output data by the hyperparameter-optimized machine learning prediction model when predicting the average erosion rate of the wall of a series bend.

[0059] Figure 10 This invention provides the prediction and confidence interval of the output data by the hyperparameter-optimized machine learning prediction model when predicting the maximum erosion rate of the upstream bend in this embodiment of the invention.

[0060] Figure 11 This invention provides the prediction and confidence interval of the output data by the hyperparameter-optimized machine learning prediction model when predicting the maximum erosion rate of the downstream bend in an embodiment of the invention.

[0061] Figure 12 This invention provides an example of how five features influence the model prediction results when predicting the average erosion rate of the wall of a series bend.

[0062] Figure 13 In this embodiment of the invention, the influence of five features on the model prediction results is shown in terms of direction and magnitude when predicting the maximum erosion rate of the upstream bend.

[0063] Figure 14 In this embodiment of the invention, the influence of five features on the model prediction results is shown in terms of direction and magnitude when predicting the maximum erosion rate of the downstream bend.

[0064] Figure 15 This is a graph showing the residual normal distribution of the BBD-RSM model and a comparison between the predicted and actual values ​​of the BBD-RSM model when predicting the average erosion rate of the wall of a series bend in an embodiment of the present invention.

[0065] Figure 16 This is a graph showing the residual normal distribution of the BBD-RSM model and a comparison between the predicted and actual values ​​of the BBD-RSM model when predicting the maximum erosion rate of the upstream bend in an embodiment of the present invention.

[0066] Figure 17 This is a graph showing the residual normal distribution of the BBD-RSM model and a comparison between the predicted and actual values ​​of the BBD-RSM model when predicting the maximum erosion rate of the downstream bend in an embodiment of the present invention.

[0067] Figure 18This is a schematic diagram illustrating the influence of two other factors on the maximum erosion rate of the elbow when any two of the following factors—inner diameter, ratio of elbow curvature radius to elbow distance, solid particle velocity, and solid particle mass flow rate—are fixed in an embodiment of the present invention. Detailed Implementation

[0068] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0069] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0070] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one" or similar expressions refer to any combination of these items, including any combination of singular or plural items. For example, "at least one of a, b, or c" can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0071] The present invention aims to provide a multi-scale erosion analysis method, system and terminal for series bends, which can predict the erosion rate of series bends with high accuracy and analyze the factors and their influence on the erosion rate of series bends at multiple scales. This solves the problem that existing technologies are unable to accurately predict the erosion of pipelines by gas-dominated solid particles, and fills the gap in the current state of research on erosion prediction and analysis of series bends.

[0072] In a first aspect, embodiments of the present invention provide a multi-scale cascaded pipe erosion analysis method, see [link to relevant documentation]. Figure 1 It includes the following steps:

[0073] S1. Obtain n sets of initial data based on the Latin hypercube sampling method;

[0074] The Latin hypercube sampling method is a hierarchical stochastic process that provides an efficient method for sampling variables from a given distribution. The Latin hypercube sampling method requires sampling N variables from a specified distribution for each k variable X1, X2, ..., Xk. s Values ​​are sampled. The cumulative distribution of each variable is divided into N equally probable intervals. A value is randomly selected from each interval. The N values ​​obtained for each variable are then randomly paired with other variables. Compared to simple random sampling, this particular strategy ensures comprehensive coverage of the entire range of each variable by maximizing the effective stratification of each marginal distribution.

[0075] As an example, the Latin hypercube sampling method was used to obtain n sets of initial data. Each set of initial data included five factors: elbow distance, elbow radius of curvature, elbow inlet velocity, particle size, and relative volume fraction of discrete phase. The value range of each factor is shown in Table 1.

[0076] Table 1. Value range for each factor

[0077] factor symbol unit Range of values Bend distance D mm 152.4～1143 Elbow curvature radius R mm 76.2～381 elbow inlet speed V m / s 5～50 Particle size <![CDATA[d0]]> μm 10～500 Discrete phase relative volume fraction φ ％ 1～10 Total flow Q kg / s Calculations based on the actual model

[0078] After Latin hypercube sampling, 221 sets of operating parameters were obtained, and their values ​​are distributed as follows: Figure 2 As shown in the figure, each variable takes values ​​uniformly within its range, ensuring the randomness of the dataset.

[0079] S2. Configure the simulation experiment and obtain n sets of simulation data based on n sets of initial data;

[0080] As one possible approach, simulation experiments include fluid flow modeling and particle trajectory tracking;

[0081] Fluid flow modeling includes: treating the gas as a continuous phase, using the Reynolds stress model as the turbulence model, and employing a reinforced wall treatment method for near-wall treatment;

[0082] As an example, considering the gas as a continuous phase, the airflow in the bend follows the continuity and momentum equations as follows:

[0083]

[0084] In the formula, ρ represents the gas density. The vector represents the velocity of the gas, P represents pressure, and τ represents stress tension. Represents volume force. The additional momentum of the solid particle is represented by μ, the gas viscosity is represented by I, the unit tensor is represented by t, and time is represented by t.

[0085] To accurately simulate turbulent flow, considering the diversity of flow directions within the computational domain and the potential for secondary flows after bends, this embodiment selects the Reynolds stress model (RSM) as the turbulence model for the simulation experiment. The RSM can more accurately capture the anisotropy and complexity of the flow under conditions of changing flow directions and the presence of secondary flows. The time-averaged mass and momentum conservation for turbulent incompressible fluid flow are as follows:

[0086]

[0087] Among them, u i x represents the average flow velocity. i The values ​​represent position, time, average pressure, gas density, kinematic viscosity, and R. ij This represents the Reynolds stress tensor.

[0088] To calculate the Reynolds stress tensor, the RSM model provides four transport equations, which are calculated as follows:

[0089]

[0090] Where P represents the amount of wave kinetic energy generated. σ represents the viscosity of the turbulent (eddy current) flow, k represents the wave kinetic energy, and σ represents the kinetic energy of the wave. k =1, C1=1.8, C2=0.6 are empirical constants, ε represents the turbulent dissipation rate, and the transport equation for the turbulent dissipation rate ε is:

[0091]

[0092] Where k represents the wave kinetic energy, ε represents the turbulent dissipation rate, and σ ε =1.3, C 1ε =1.44, C 2ε =1.92 is an empirical constant.

[0093] After constructing the turbulence model, the next crucial step is to select an appropriate near-wall treatment strategy. This embodiment employs an enhanced wall treatment method, which demonstrates higher efficiency than traditional modeling techniques in resolving boundary layer-related issues. The advantage of the enhanced wall treatment method lies in its ability to provide more accurate data when simulating near-wall flow. However, near-wall treatment requires the use of more boundary layer meshes.

[0094] This embodiment uses the Lagrangian method for particle trajectory tracking, considering drag, gravity, and lift, but neglecting pressure gradient force and virtual mass force, and using the normal e. n and tangential e t The wall recovery coefficient method is used to establish a springback model;

[0095] As an example, in a Lagrange reference frame, the particle trajectory is calculated by integrating over the force balance on the particle. The particle's position and equations of motion are shown below:

[0096]

[0097] Where, x p v represents the particle's position. p ρ is the particle velocity. p For particle density, μ f Let d be the fluid viscosity. p C is the particle diameter. D R is the drag coefficient. ep C is the particle Reynolds number. VM This is a virtual quality factor, and its value here is 0.5.

[0098] According to Newton's second law, the governing equations for the particle's motion are:

[0099]

[0100] Where, m p Let v be the particle mass, u be the fluid velocity, and v be the fluid velocity. p For particle velocity, Indicates resistance. F represents gravity. A Additional forces, including pressure gradient force F P Virtual mass force F VM Saffman Lift F S .

[0101] Apart from gravity, all these forces are interphase forces. Among them, drag plays a dominant role in particle motion. Because the density ratio of the fluid to the particles is very small, the magnus force and basset force can be ignored. This embodiment uses an aspherical drag coefficient with a shape factor of 0.8. Therefore, the drag coefficient C of the spherical particles is... D It can be defined as:

[0102]

[0103] Among them, b1, b2, b3, and b4 are constants based on the particle's sphericity (φ), used to explain the particle's shape.

[0104] b1=exp(2.3288―6.4581φ+2.4486φ 2 )

[0105] b2 = 0.0964 + 0.5565φ

[0106] b3=exp(4.905―13.8944φ+18.4222φ2 ―10.2599φ 3 )

[0107] b4=exp(1.4681+12.2584φ―20.7322φ 2 +15.8855φ 3 )

[0108]

[0109] Where s is the surface area of ​​a sphere with the same volume as the particle, and S is the actual surface area of ​​the particle.

[0110] Saffman Lift F S The definition is as follows:

[0111]

[0112] Where, K = 2.594, d ij The Saffman lift is a deformation tensor. Only at submicron particles and low Reynolds numbers is the motion of the particle significantly affected by the Saffman lift, therefore the Saffman lift can be ignored.

[0113] Pressure gradient force F P Represented as:

[0114]

[0115] Virtual mass force F VM Represented as:

[0116]

[0117] In the formula, C VM This represents the virtual mass factor, which only occurs when the density ratio is... The influence of these two forces only becomes significant when the value is greater than 0.1. In practical applications, the density of particles is much greater than that of air. Therefore, the pressure gradient force and the virtual mass force can be ignored.

[0118] Through the aforementioned flow field modeling and particle tracking, impact information, including impact velocity and impact angle, can be obtained. This data is then combined with the erosion model to calculate the erosion rate of the pipe wall / surface.

[0119] This embodiment uses the Finnie erosion model as the erosion model. The Finnie erosion model can be expressed as:

[0120]

[0121] Where k is a constant, V pLet f(θ) be the particle incident velocity, f(θ) be the incident angle function, and θ be the angle between the particle trajectory and the wall. In this embodiment, the pipe density is taken as 7990 kg / m³. 3 .

[0122] Next, boundary conditions were set, and the flow simulation was performed in Fluent ANSYS 2022 R1, using air (gas) as the carrier fluid. The density and viscosity of air were 1.225 kg / m³. 3 And 1.789E-05 kg / m·s. A pressure-based steady-state flow simulation was chosen, with gravity acting in the Z direction (-9.81 m / s). 2 The convergence residual is set to less than 10. -3 The SIMPLE algorithm was chosen to couple pressure and velocity. A second-order scheme was used for discrete pressure, momentum equations, dissipation rate, and turbulent kinetic energy, while a first-order scheme was used for the Reynolds stress equation. The simulation was conducted at atmospheric pressure (115.1 kPa). In this embodiment, velocity inlet and pressure outlet conditions were considered at the inlet and outlet boundaries, respectively, with no wall slippage. During the simulation, the flow solution was first obtained, and then particles were injected into the inlet of the computational domain. The particle distribution was random, and the particle velocity was the same as the fluid velocity. In this embodiment, the particle volume concentration was very small. Therefore, it was assumed that the influence of particles on the flow was negligible, and unidirectional coupling was used in particle tracking.

[0123] During erosion, solid particles inevitably undergo energy conversion upon collision with the pipe wall, and the rebound velocity of the particles will be lower than the incident velocity. This energy conversion is typically described by the ratio of the velocity components (i.e., the coefficient of restitution). The coefficient of restitution can be set as a function of the angle θ between the particle trajectory and the wall surface; in this embodiment, the normal angle θ is used. n and tangential e t The method for calculating the wall recovery coefficient is as follows:

[0124] e n =0.993―0.0307θ+0.000475θ 2 —2.61×10 ―6 θ 3

[0125] e t =0.988―0.029θ+0.000643θ 2 —3.56×10 ―6 θ 3 .

[0126] S3. Select a machine learning model and optimize its hyperparameters using a grid search method;

[0127] As one possible implementation, the machine learning model is the CatBoost model, with hyperparameters including learning rate, depth, and L2 regularization parameter. The CatBoost model has two main advantages: first, it can automatically handle categorical features; second, it binarizes floating-point features, statistical values, and one-hot encoded features. The main parameters of the CatBoost model are roughly the same as those of the XGBoost and LightBGM models, the main difference being that the CatBoost model allows for the definition of the tree growth strategy.

[0128] There are two different approaches: SymmetricTree and Depthwise. The SymmetricTree growth strategy builds the tree layer by layer until a specified depth is reached. In each iteration, all leaves at the last tree level are split under the same conditions, and the resulting tree structure is always symmetrical. The Depthwise growth strategy builds the tree layer by layer until a specified depth is reached. In each iteration, all non-terminal leaves from the last tree level are split, and each leaf is split according to the condition that best improves the loss.

[0129] The `Max_leaves` parameter controls the minimum number of training samples in a leaf. If the sample count is less than the specified value, CatBoost will not search for new splits in the leaves and can only be used under the Depthwise growth strategy.

[0130] Since the setting of various parameters of the model can have a great impact on the prediction efficiency for different datasets, this embodiment uses the grid search method to optimize the hyperparameters of the machine learning model. The grid search includes the following steps: defining the model, determining the hyperparameters, creating a parameter grid, setting the evaluation criteria, using the grid search, performing the search, selecting the best parameters, and retraining the model.

[0131] S4. Train a machine learning model based on multiple sets of simulation data to obtain a hyperparameter-optimized machine learning prediction model; the hyperparameter-optimized machine learning prediction model is specifically as follows:

[0132] M = CatBoost[D Train ,θ * (a,b,c)]

[0133] Among them, D Train Let θ represent the training set in n sets of simulation data. * Let (a,b,c) represent the optimal parameters, and let (a,b,c) represent the CV parameter search space, where the CV parameters are k∈{1,2,3,4,5}.

[0134] To compare the prediction models, 221 datasets were divided into training and test sets in an 8:2 ratio. Random Forest (RF), LightBGM, AdaBoost, XGBoost, and CatBoost models, all optimized with grid search hyperparameters, were constructed respectively, with the coefficient of determination (R²) used as the benchmark. 2 The superior performance of the CatBoost model used in this embodiment of the invention compared to other models is evaluated using three metrics: root mean square error (RMSE), mean absolute error (MAE), and mean square error (MSE). The model output is the maximum erosion rate, expressed in kg / m³. 2 s. See comparison results. Figures 3 to 5 , Figure 3 The performance of each model in predicting the average erosion rate of the wall of a series-connected bend is presented. It can be seen that the CatBoost model has the lowest error, with a root mean square error of 5.38e-04 and a mean absolute error of 3.28e-04. Its coefficient of determination reaches 0.99, the highest among all models, indicating that this model predicts almost all the data and performs best. The LightBGM and AdaBoost models have lower coefficients of determination, both around 0.92, indicating weaker fitting ability. Figure 4 The performance of each model in predicting the maximum erosion rate of the upstream bend is demonstrated. The CatBoost model again performs exceptionally well, with a root mean square error (RMSE) of 1.67e-01 and a mean absolute error (MAE) of 1.03e-01. It also boasts the highest coefficient of determination (CDO) of 0.95, indicating its superior performance in predicting the maximum erosion rate of the upstream bend. The LightBGM model has the lowest CDO at 0.79, reflecting its weaker fitting ability in this task. The AdaBoost model also has a relatively large error, with an RMS of nearly 4.30e-01. Other models (such as the XGBoost model) have CDO values ​​around 0.88, indicating moderate performance. Figure 5 The performance of various models in predicting the maximum erosion rate of downstream bends is demonstrated. In this task, the optimized CatBoost model and the Random Forest model have the lowest errors, with root mean square errors of 2.64e-01 and 2.62e-01, respectively. The Random Forest model achieves a determination coefficient of 0.90, demonstrating excellent performance; the optimized CatBoost model has a slightly lower determination coefficient of 0.89, but it is still better than the other models. The AdaBoost model has the lowest determination coefficient in this task, at only 0.70, indicating its poor fit in this scenario. The LightBGM and XGBoost models also have relatively high errors, especially the LightBGM model with a root mean square error of 3.49e-01.

[0135] In summary, the CatBoost model of this invention performs well in all tasks, especially in predicting the average erosion rate of the wall of a series bend, where it has the lowest error and the highest coefficient of determination.

[0136] S5. Predicting the erosion rate of series bends using a hyperparameter-optimized machine learning prediction model;

[0137] As one possible implementation, S5 adopts the following method:

[0138]

[0139] in, The value represents the predicted erosion rate of the series bend, where D represents the bend distance, R represents the bend radius of curvature, V represents the bend inlet velocity, d0 represents the particle size, Q represents the total flow rate, and M represents the hyperparameter-optimized machine learning prediction model.

[0140] See Figures 6 to 8 To optimize the accuracy of the machine learning prediction model for regression prediction on three tasks, the following tasks were identified: Task 1: Prediction of the average erosion rate of the wall of the series bend; Task 2: Prediction of the maximum erosion rate of the upstream bend; and Task 3: Prediction of the maximum erosion rate of the downstream bend. Figures 9 to 11 This figure illustrates the predictions and confidence intervals of a hyperparameter-optimized machine learning prediction model for the output data under three tasks. The horizontal axis represents the test sample number, and the vertical axis represents the output. The elements in the figure can be analyzed as follows: The red dots represent the test data, i.e., the actual observations of the model. These data points provide a benchmark for the model's predictions, facilitating the evaluation of the model's performance. The dark blue curve represents the prediction mean μ of the hyperparameter-optimized machine learning prediction model. This curve shows the model's prediction result for each test sample, and comparing it with the red data points helps to observe the model's fit. Different shades of blue shading represent confidence intervals, which provide a quantitative representation of the uncertainty in the model's predictions. Overall, the figure shows the fit of the hyperparameter-optimized machine learning prediction model to the data; most predictions are close to the actual data, while also capturing significant fluctuations.

[0141] S6. Multi-scale analysis of the factors influencing the erosion rate of the tandem bend and their degree of influence, obtaining analytical results. Multi-scale analysis includes: SHAP analysis, response surface methodology, and Stokes equation analysis. The analytical results are as follows:

[0142]

[0143] in, This indicates the SHAP analysis results. This indicates the degree of influence of the interaction between any two factors. Effect(d0→pi) indicates the degree of influence of particle size on the upstream or downstream bend.

[0144] As one possible implementation, SHAP analysis can be performed using the following method:

[0145]

[0146] Where i∈{1,2}, p1 represents the upstream bend, and p2 represents the downstream bend. φ(M) represents the SHAP analysis result, which is the SHAP value calculation function based on the hyperparameter optimization machine learning prediction model. D represents the bend distance, R represents the bend curvature radius, V represents the bend inlet velocity, d0 represents the particle size, Q represents the total flow rate, j represents the j-th set of simulation data, 1≤j≤n, and n represents the n-th set of simulation data.

[0147] As an example, the SHAP value can be calculated by considering the marginal contributions of feature values ​​in different feature subsets and then averaging these marginal contributions. It should be noted that some features may not be the direct cause of the erosion rate, but are related to erosion. The SHAP value is then used to evaluate the contribution of each feature value to the erosion rate. This embodiment uses the SHAP library in Python to calculate the SHAP value; see [link to documentation]. Figures 12 to 14 The graph illustrates the impact of five features (total flow rate Q, elbow inlet velocity V, particle size d0, elbow radius of curvature R, and elbow distance D) on the model output under three tasks. The SHAP value is used to quantify the contribution of each feature. The horizontal axis in the graph represents the SHAP value, showing the direction and magnitude of the feature's influence on the model's prediction results. A positive SHAP value indicates a positive impact of the feature on the model output, while a negative value indicates the opposite. Figures 12 to 14 Among the features, Q and V have the most significant impact on the model output, and their SHAP values ​​are widely distributed, indicating a large contribution to the prediction results. High values ​​of feature Q (red) generally increase the model output, while low values ​​(blue) decrease the output. High values ​​of feature V have a similar positive effect, while low values ​​decrease the model's prediction. Figure 12 and Figure 13 The influence of feature d0 is relatively small, with a narrow range of SHAP values, indicating its limited impact on the model output. Features R and D have even weaker effects, having almost no significant positive or negative impact on the model output, although low and high values ​​still have some minor effect on model prediction. The color gradient in the legend illustrates the magnitude of each feature value, with high values ​​in red and low values ​​in blue. Overall, the relationship between color and SHAP values ​​suggests that increasing the feature value will affect the SHAP value positively or negatively, thus impacting the model prediction results.

[0148] exist Figures 12 to 14In the SHAP analysis, significant differences were observed between the upstream and downstream bend locations in their impact on the maximum erosion rate in the gas-solid flow system, particularly in the order of influence of particle size d0 and bend inlet velocity V. At the upstream bend, the inlet velocity V had a more significant impact on the erosion rate, while at the downstream bend, the influence of particle size d0 increased, exceeding that of the inlet velocity V. This phenomenon is similar to the results of correlation analysis. This phenomenon can be further analyzed from the following aspects:

[0149] First, analyzing the changes in flow state, significant changes in flow state occur in the gas-solid fluid system as it passes through the bends. At the upstream bend, due to the relatively uniform fluid mixing, the inlet velocity V contributes significantly to the erosion rate. However, after passing through the upstream bend, the flow field changes, and the flow characteristics of the solid particles also change accordingly. At this point, the impact of particles on the wall may be more significant, causing the SHAP value of the particle size d0 at the downstream bend to exceed the SHAP value of the inlet velocity V.

[0150] Second, due to differences in erosion mechanisms, particles of different sizes may trigger different forms of erosion during gas-solid two-phase flow erosion. At the upstream bend, the inlet velocity V dominates the erosion rate; while at the downstream bend, the velocity effect weakens, and the reduced velocity leads to a decrease in the effect of large-diameter particles, while small-diameter particles cause more erosion on the wall, thus making the influence of particle size d0 exceed that of the inlet velocity V.

[0151] Third, considering the effects of particle deposition and geometric characteristics, after the gas-solid flow passes through the upstream bend, some large-diameter particles may deposit on the inner wall of the bend. The location and geometry of the downstream bend determine the gas-solid flow behavior at this location, which differs significantly from that of the upstream bend. At the downstream bend, particle deposition and impact have a more significant impact on erosion, enhancing the relative importance of particle size d0 at this location.

[0152] Fourth, regarding feature interaction effects, significant interaction effects may exist between different features at different bend locations. For upstream bends, erosion depends more on the inlet velocity; the interaction between the bend inlet velocity V and particle size d0 is relatively small. However, at downstream bends, the effect of the bend inlet velocity V weakens, making the contribution of particle size more significant. Additionally, the interaction between particle size and other features (such as the bend inlet velocity V and the bend curvature radius R) may be more pronounced at this location.

[0153] As one possible implementation, response surface methodology is adopted:

[0154]

[0155] Where i∈{1,2}, p1 represents the upstream bend, p2 represents the downstream bend, x,y∈(D,R,V,d0,Q) and x≠y, D represents the bend distance, R represents the bend radius of curvature, V represents the bend inlet velocity, d0 represents the particle size, and Q represents the total flow rate. It represents the degree of influence of the interaction between any two factors; RSM stands for Response Surface Analysis.

[0156] As an example, this embodiment employs a Box-Behnken (BBD) design strategy for response surface analysis. The BBD treatment combination is located at the center point of the test space edge, requiring at least three factors, each with only three levels to ensure that no factors are simultaneously set at high levels. Response surface design can be used to evaluate the nonlinear effects of factors and first- and second-order coefficients. Based on the single-action analysis results and the actual engineering conditions of the gas-solid series bend, particle size, bend distance, bend radius of curvature, bend inlet velocity, and total flow rate are selected as factors in the Box-Behnken design-response surface method (BBD-RSM). The factor and level settings of the BBD-RSM model are shown in Table 1.

[0157] Table 1. Factor and level settings for the BBD-RSM model.

[0158]

[0159] The BBD-RSM model scheme and calculation results are shown in Table 2:

[0160] Table 2. BBD-RSM Model Scheme and Calculation Results

[0161]

[0162]

[0163]

[0164] The analysis of variance is shown in Table 3:

[0165] Table 3 shows the results of the analysis of variance for each indicator.

[0166]

[0167]

[0168] A p-value less than 0.0500 indicates that the model terms are significant. As can be seen in Table 3, in Tasks 1 to 3, the p-value of the BBD-RSM model designed in this embodiment of the invention is less than 0.0001, indicating that the model has high significance and good adaptability.

[0169] For the average erosion rate of the wall, the interaction term DE is significant for particle size (A), elbow inlet velocity (D), and total flow rate (E). For the maximum erosion rate of the upstream elbow, the interaction terms AD, AE, and DE are all significant for particle size (A), elbow inlet velocity (D), and total flow rate (E). For the maximum erosion rate of the upstream elbow, the interaction terms AC, AD, and DE are all significant for particle size (A), velocity (D), and total flow rate (E). Among the output values ​​related to the erosion rate of the three tasks, the quadratic term A... 2 D 2 All were significant.

[0170] See Figures 15 to 17 The residual normal distribution plots of the BBD-RSM model in the three tasks, and the comparison plots between the predicted and actual values ​​of the BBD-RSM model. Figure 15 (a) Figure 16 (a) and Figure 17 (a) shows that the residuals of the BBD-RSM model in the three tasks are linear and uniformly distributed, indicating that the model is adaptive; Figure 15 (b) Figure 16 (b) and Figure 17 Figure (b) shows that the BBD-RSM model has high prediction accuracy in the three tasks.

[0171] See Figure 18 This shows the influence of two factors on the maximum erosion rate of the elbow when any two of the inner diameter, R / D ratio, and solid particle velocity and mass flow rate are fixed. The steeper the three-dimensional graph of the response surface, the more significant the influence on the maximum erosion rate. The shape of the contour plot formed by projecting the response surface onto the bottom surface can reflect the interaction between factors; that is, elliptical contour lines indicate significant interaction between factors, while straight lines indicate insignificant interaction. For the upstream bend, in Figure 18 Algebra (a) shows the significant influence of the interaction between particle diameter and gas-solid velocity on the erosion rate. Larger particles exert a greater impact on the pipe wall at higher velocities, leading to a higher erosion rate. Furthermore, the synergistic effect between particle diameter and flow velocity rapidly increases the erosion rate. Figure 18 In (b), the interaction between particle diameter and solid particle flow rate also significantly affects the maximum erosion rate. When the particle diameter is small, the change in flow rate has a limited effect on the erosion rate, but when the particle diameter is large, a higher solid particle flow rate significantly increases the erosion rate. This interaction indicates that the erosion risk increases sharply when large particles and high flow rates are present simultaneously. Figure 18Figure (c) shows the effect of the interaction between gas-solid velocity and particle flow rate on the erosion rate. High velocity increases particle kinetic energy, while high flow rate means more particles will impact the pipe wall. The synergistic effect of these two factors leads to a higher impact frequency and force, thus exacerbating erosion. For downstream bends, in Figure 18 As shown in (d), the erosion rate gradually increases with increasing particle size, especially when the bend radius is small, where the erosion is more severe. Figure 18 As can be seen in (e), the interaction between gas-solid velocity and particle size has no significant effect on the downstream bend erosion rate. Figure 18 In the middle (a) section, the interaction between gas-solid velocity and particle size has a significant impact on the erosion rate of the upstream bend, but the trends are similar. Figure 18 The performance of (f) and Figure 18 Similar to (c).

[0172] Through interaction analysis, this invention provides a better understanding of how these factors collectively affect pipeline erosion rates, thereby offering more precise operational guidance and equipment design solutions.

[0173] As one possible implementation, the Stokes equations analysis is performed using the following method:

[0174]

[0175] Where, ρ p d represents particle density. p Let μ represent the particle diameter, u represent the fluid velocity, μ represent the fluid dynamic viscosity, and D represent the pipe diameter. The influence of particle size on upstream or downstream bends is as follows:

[0176]

[0177] Among them, Effect(d0→p1) represents the degree of influence of particle size on the upstream bend, and Effect(d0→p2) represents the degree of influence of particle size on the downstream bend.

[0178] As an example, the acceleration characteristics of gases on particles of different sizes vary, leading to different particle velocities and ultimately different erosion rates. The Stokes number represents the ratio of the relaxation time of a solid particle to the characteristic time of the fluid. It reflects the correlation between the inertial force and drag of the solid particle. Furthermore, it is a dimensionless number reflecting the curvilinear motion of particles. When the Stokes number is less than 1, particles easily follow the surrounding fluid. When the Stokes number is much greater than 1, the influence of the fluid on particle motion becomes smaller. The following discussion uses two typical operating conditions, Condition A and Condition B, as examples. The Stokes numbers for Condition A and Condition B are shown in Table 4.

[0179] Table 4. Stokes Numbers for Operating Conditions A and B

[0180]

[0181]

[0182] The Stokes number for condition A is 1.11. As particle size increases, the Stokes number also increases, reaching 194.18 for condition B, significantly greater than 1. This means that under condition B, the gas cannot easily carry solid particles. Combined with statistical analysis using Facet Maximum-all, it can be found that at the upstream bend, larger particles cause a higher erosion rate compared to smaller particles. This is because particles of different sizes enter at the same velocity, and larger particles have higher kinetic energy when colliding with the wall. Therefore, larger particles cause greater damage at the upstream bend. Conversely, at the downstream bend, large particles cause less erosion. Larger particles collide and lose kinetic energy at the upstream bend, and due to the high Stokes number, the gas has poor mobility for these large particles. Therefore, at the downstream bend, erosion caused by large particles is less. Therefore, in condition A, small-diameter particles can be accelerated by the gas, resulting in greater damage at the downstream bend than at the upstream bend compared to the damage caused by large-diameter particles in condition B. Among the factors influencing the maximum erosion rate at the downstream bend, the effect of particle size is more pronounced than at the upstream bend.

[0183] The following examples illustrate the practical application of this solution:

[0184] Example 1 (Small-diameter particles dominate downstream erosion):

[0185] (1) Specific operating conditions:

[0186] Elbow distance: 572.75mm

[0187] Elbow radius: 364.19mm

[0188] Inlet velocity: 25.56 m / s

[0189] Particle size: 11.58 μm

[0190] Total flow rate: 18.81 kg / s

[0191] Stokes number: 1.11 (Stk≈1, particles are easily moved by airflow).

[0192] (2) SHAP analysis:

[0193] Upstream bend (p1): The highest SHAP values ​​for gas-solid velocity (V) and total flow rate (Q) (V: +0.85, Q: +0.78) indicate that high-speed airflow and high flow rate jointly drive erosion;

[0194] Downstream bend (p2): The SHAP value of particle size (d0) is significantly increased (+0.62), much higher than that upstream (+0.08), indicating that small particles are more easily carried downstream due to their low inertia, leading to increased erosion at the downstream bend.

[0195] (3) Response Surface Analysis

[0196] Interaction: Response surface of d0 and V ( Figure 18 As shown in (a), when d0 = 11.58 μm and V = 25.56 m / s, the downstream bend erosion rate (0.372 kg / m) is... 2 The ·s) was significantly higher than that of the upstream bend (0.187 kg / m). 2 ·s);

[0197] Contour shape: Elliptical contour lines indicate that the interaction between d0 and V is more significant at the downstream bend (R). 2 =0.89).

[0198] (4) Stokes equation analysis:

[0199] Particle behavior: Stk = 1.11 (<1), small particles follow the airflow fully, and the high velocity causes a brief impact at the upstream bend, while the cumulative effect at the downstream bend leads to enhanced erosion.

[0200] Erosion mechanism: Small particles are affected by secondary flow at the downstream bend and collide with the pipe wall, forming a localized high erosion area.

[0201] Example 2 (Large-diameter particles dominate upstream erosion):

[0202] (1) Specific operating conditions:

[0203] Elbow distance: 558.77mm

[0204] Elbow radius: 333.11mm

[0205] Inlet velocity: 35.81 m / s

[0206] Particle size: 129.08μm

[0207] Total flow rate: 14.04 kg / s

[0208] Stokes number: 194.18 (Stk>>1, particle inertia dominates).

[0209] (2) SHAP analysis:

[0210] Upstream bend (p1): The SHAP value of particle size (d0) is the highest (+1.32), far exceeding that of velocity (V:+0.76), indicating that the impact kinetic energy of large particles is the main cause of erosion in the upstream bend.

[0211] Downstream bend (p2): The SHAP value of the total flow (Q) decreases (+0.43) as the impact of large particles on the downstream bend is weakened after the kinetic energy is lost at the upstream bend.

[0212] (3) Response Surface Analysis

[0213] Interaction: Response surface of d0 and Q ( Figure 18 Figure (b) shows that when d0 = 129.08 μm and Q = 14.04 kg / s, the erosion rate of the upstream bend is 0.908 kg / m. 2 The ·s) is 1.5 times that of the downstream bend.

[0214] (4) Stokes equation analysis:

[0215] Particle behavior: Stk = 194.18 (>>1), large particles have high inertia and directly impact the pipe wall at the upstream bend, rapidly dissipating kinetic energy, resulting in a reduced erosion rate at the downstream bend (0.603 kg / m). 2 ·s);

[0216] Erosion mechanism: Large particles collide at the upstream bend due to high speed and high kinetic energy, forming deep erosion pits.

[0217] Example 3 (Combined effect of medium speed and medium particle size):

[0218] (1) Specific operating conditions:

[0219] Elbow distance: 647.70mm

[0220] Elbow radius: 228.60mm

[0221] Inlet velocity: 27.50 m / s

[0222] Particle size: 255.00 μm

[0223] Total flow rate: 25.50 kg / s

[0224] Stokes number: 87.45 (Stk>1, part of the particles follow the airflow).

[0225] (2) SHAP analysis:

[0226] Upstream bend (p1): The SHAP values ​​of total flow (Q) and velocity (V) are balanced (Q: +0.91, V: +0.88), indicating that flow and velocity jointly drive erosion;

[0227] Downstream bend (p2): The SHAP value of the bend radius (R) is significantly negative (-0.55), indicating that the smaller radius leads to turbulent flow field at the downstream bend and intensifies erosion.

[0228] (3) Response Surface Analysis

[0229] Interaction: Response surface of R and V ( Figure 18 The diagram (d) shows that when R = 228.60 mm and V = 27.50 m / s, the downstream bend erosion rate is 0.353 kg / m. 2 •s) increases due to enhanced secondary flow;

[0230] Contour shape: Dense ellipses indicate that the interaction between R and V has a significant impact on downstream bend erosion (R 2 =0.85).

[0231] (4) Stokes equation analysis:

[0232] Particle behavior: Stk=87.45(>1), some particles deviate from the airflow trajectory, causing moderate impact at the upstream bend due to moderate velocity, and enhanced secondary flow at the downstream bend due to the small bend radius, resulting in erosion distribution and diffusion;

[0233] Erosion mechanism: Medium-speed airflow carries medium-sized particles to form a dispersed impact pattern, and erosion in the upstream and downstream tends to be balanced.

[0234] The multi-scale erosion analysis method for series bends proposed in this embodiment can predict the erosion rate of series bends with high accuracy using the CatBoost model. Through SHAP analysis, response surface analysis, and Stokes equation analysis, the intrinsic relationship between the model's erosion rate prediction and the prediction of gas-solid erosion in series bends can be further explained, increasing the ability to predict industrial pipeline erosion data in real time and its interpretability.

[0235] Secondly, the present invention provides a multi-scale series bend corrosion analysis system, comprising:

[0236] The simulation data acquisition unit is used to acquire n sets of initial data based on the Latin hypercube sampling method, configure the simulation experiment, and obtain n sets of simulation data based on the n sets of initial data.

[0237] The hyperparameter-optimized machine learning prediction model acquisition unit is used to select a machine learning model, optimize the hyperparameters of the machine learning model based on the grid search method, train the machine learning model based on simulation data, and obtain the hyperparameter-optimized machine learning prediction model.

[0238] A series bend erosion rate prediction unit is used to predict the erosion rate of series bends based on a hyperparameter-optimized machine learning prediction model.

[0239] The erosion analysis unit for tandem bends is used for multi-scale analysis of the factors and their influence on the erosion rate of tandem bends, and to obtain analysis results. The multi-scale analysis includes: SHAP analysis, response surface analysis, and Stokes equation analysis.

[0240] Thirdly, the present invention provides a terminal including a processor and a communication interface coupled to the processor, the processor being used to run computer programs or instructions to implement the multi-scale series bend erosion analysis method provided in the first aspect.

[0241] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the description of the drawings, in carrying out the claimed invention. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple components. A single processor or other unit can implement several of the functions listed in the specification. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0242] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the invention and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications fall within the scope of the invention and its equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A multi-scale cascaded pipe erosion analysis method, characterized in that, Includes the following steps: S1. Acquisition based on Latin hypercube sampling method Initial group data; S2. Configure simulation experiments, based on the above. Initial data of the group Group simulation data; S3. Select a machine learning model and optimize its hyperparameters using a grid search method; S4. Train the machine learning model based on the simulation data to obtain a hyperparameter-optimized machine learning prediction model; S5. Predict the erosion rate of the series bend based on the hyperparameter-optimized machine learning prediction model; S6. A multi-scale analysis was conducted to determine the factors influencing the erosion rate of the tandem bend and their extent of influence, yielding analytical results. This multi-scale analysis included: SHAP analysis, response surface methodology, and Stokes equation analysis. The analytical results are as follows: in, This indicates the SHAP analysis results. This indicates the degree of influence of the interaction between any two factors. This indicates the degree of influence of particle size on the upstream or downstream bend of the pipe. , Indicates the upstream bend. Indicates the downstream bend. and , Indicates the distance to the bend. Indicates the radius of curvature of the elbow. Indicates the inlet velocity of the bend. Indicates particle size, This indicates the total flow rate.

2. The multi-scale series bend corrosion analysis method according to claim 1, characterized in that, SHAP analysis is performed using the following method: This is a function for calculating the SHAP value of a machine learning prediction model based on hyperparameter optimization. Indicates the first Set of simulation data, 1 .

3. The multi-scale series bend corrosion analysis method according to claim 1, characterized in that, The following method is used to implement response surface analysis: in, This represents response surface analysis.

4. The multi-scale tandem bend erosion analysis method according to claim 1, characterized in that, The Stokes equations are analyzed using the following method: in, Indicates particle density, Indicates particle diameter, Indicates fluid velocity. Indicates fluid dynamic viscosity, The following indicates the degree to which pipe diameter and particle size affect upstream or downstream bends: in, This indicates the degree of influence of particle size on the upstream bend. This indicates the degree of influence of particle size on the downstream bend.

5. The multi-scale tandem bend erosion analysis method according to claim 1, characterized in that, The machine learning model is a CatBoost model, and the hyperparameters include: learning rate, depth, and L2 regularization parameter; the hyperparameter optimization of the machine learning prediction model specifically involves: in, express The training set in the set of simulation data, Indicates the optimal parameters. This represents the CV parameter search space, where the CV parameters are... .

6. The multi-scale tandem bend erosion analysis method according to claim 5, characterized in that, S5 is implemented using the following method: in, This represents the predicted erosion rate of the series bend. This refers to hyperparameter optimization of machine learning prediction models.

7. The multi-scale tandem bend erosion analysis method according to claim 1, characterized in that, The simulation experiments include fluid flow modeling and particle trajectory tracking; The fluid flow modeling includes: treating the gas as a continuous phase, using the Reynolds stress model as the turbulence model, and employing a reinforced wall treatment method for near-wall treatment. Particle trajectory tracking is performed using the Lagrangian method, considering drag, gravity, and lift, but neglecting pressure gradient force and virtual mass force, and using the normal direction. and tangential The wall recovery coefficient method is used to establish a springback model; The Finnie erosion model was used as the erosion model.

8. A multi-scale series bend erosion analysis system, characterized in that, include: The simulation data acquisition unit is used to acquire data based on the Latin hypercube sampling method. Set initial data, configure simulation experiments, based on the above Initial data of the group Group simulation data; The hyperparameter-optimized machine learning prediction model acquisition unit is used to select a machine learning model, optimize the hyperparameters of the machine learning model based on the grid search method, train the machine learning model based on simulation data, and obtain a hyperparameter-optimized machine learning prediction model. A series bend erosion rate prediction unit is used to predict the erosion rate of the series bend based on the hyperparameter-optimized machine learning prediction model. The tandem bend erosion analysis unit is used for multi-scale analysis of the factors influencing the erosion rate of tandem bends and their degree of influence, obtaining analysis results. Multi-scale analysis includes: SHAP analysis, response surface methodology, and Stokes equation analysis; the analysis results are as follows: in, This indicates the SHAP analysis results. This indicates the degree of influence of the interaction between any two factors. This indicates the degree of influence of particle size on the upstream or downstream bend of the pipe. , Indicates the upstream bend. Indicates the downstream bend. and , Indicates the distance to the bend. Indicates the radius of curvature of the elbow. Indicates the inlet velocity of the bend. Indicates particle size, This indicates the total flow rate.

9. A terminal comprising a processor and a communication interface coupled to the processor, the processor being configured to run a computer program or instructions to implement a multi-scale tandem bend erosion analysis method as described in any one of claims 1 to 7.

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