Multi-scale series elbow erosion analysis method, system and terminal

Abstract

The invention belongs to the technical field of pipeline erosion prediction and evaluation, and relates to a multi-scale series elbow erosion analysis method and system and a terminal. The analysis method comprises the following steps: acquiring n groups of initial data based on a Latin hypercube sampling method; configuring a simulation experiment, and obtaining n groups of simulation data based on the n groups of initial data; selecting a machine learning model, and optimizing hyper-parameters of the machine learning model based on a grid search method; training a machine learning model based on the simulation data to obtain a hyper-parameter optimization machine learning prediction model; predicting the erosion rate of the series elbow pipe based on a hyper-parameter optimization machine learning prediction model; and performing multi-scale analysis on factors and influence degrees which influence the erosion rate of the series elbow pipe to obtain an analysis result. Through SHAP analysis, response surface analysis and Stokes equation analysis, the internal relation influencing model erosion rate prediction and influencing series elbow gas-solid erosion prediction is explained, and the real-time prediction capacity and interpretable capacity of industrial pipeline erosion are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of pipeline erosion prediction and evaluation, and in particular to a multi-scale series elbow erosion analysis method, system and terminal. Background Art

[0002] In recent years, pipeline and equipment damage caused by erosion has been on the rise. During the extraction of crude oil and natural gas from reservoirs, these fluids often carry sand and other impurities. Under high flow rates, these particles can impact the inner walls of pipelines, leading to erosion. This can also cause failures of critical equipment in the oil and gas industry, ultimately shutting down the entire production system. Notably, due to their kinetic energy, sand particles are particularly susceptible to erosion in areas where fluid dynamics vary dramatically, such as 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 not only saves oil and gas companies money but also effectively prevents the leakage of other compounds from the pipeline, thereby minimizing environmental damage. However, predicting erosion in sandy single-phase and multiphase flows is a complex problem, as the process involves numerous interacting parameters that collectively determine the extent of particle erosion on the inner walls of the pipeline. Solid particle erosion has been widely studied in the early days. 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 erosion equations, which are still quite different from the actual erosion conditions.

[0003] Researchers are still promoting empirical prediction models, but these typically use simplified models of multiphase flow to calculate the local velocities of the phases and determine the impact velocity of sand particles. Therefore, the accuracy of erosion prediction in multiphase flow is limited to the accuracy of the multiphase flow model. Furthermore, due to the limitations of experimental conditions and the multitude of 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 understand the impact of various factors on the erosion phenomenon. Currently, the mainstream approach to elbow erosion research is computational fluid dynamics (CFD). Due to the flexibility and efficiency of CFD, a large number of studies have been conducted on particle trajectories, erosion morphology, 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 extensive computing resources and time, which is not conducive to real-time analysis and optimization. With the continuous exploration of computing, artificial intelligence has been widely used in many engineering applications. Some researchers have applied machine learning methods of artificial intelligence to erosion prediction, attempting to establish corresponding erosion prediction models from a data-driven perspective. Even though artificial intelligence models perform well in processing complex data and providing accurate predictions, the decision-making process within these artificial intelligence models is usually hidden or too complex, making it difficult to explain or illustrate the models.

[0004] In summary, while existing technologies have explored pipeline erosion prediction and analysis using empirical formulas, CFD simulation analysis, and artificial intelligence algorithms, accurate predictions for gas-dominated solid particle erosion pipelines are often inadequate due to the complex flow conditions and erosion mechanisms within them. These predictions are often limited to the single effects of various factors on elbow erosion. In pipeline systems, tandem elbows present more complex flow conditions than single elbows, yet existing research on erosion prediction and analysis for tandem elbows is virtually nonexistent. Summary of the Invention

[0005] The purpose of the present invention is to address the current situation where the existing technology is difficult to accurately predict gas-dominated solid particle erosion in pipelines and the research on erosion prediction and analysis of series elbows is almost blank. The present invention proposes a multi-scale series elbow erosion analysis method, system and terminal to accurately predict the erosion rate of series elbows, analyze the factors affecting the erosion rate of series elbows and the degree of influence at multiple scales, and provide engineering guidance for preventing series elbow erosion.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

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

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

[0009] S2. Configure a simulation experiment to 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 the machine learning model based on the simulation data to obtain a hyperparameter-optimized machine learning prediction model;

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

[0013] S6. Multi-scale analysis of the factors and degree of influence on the erosion rate of the series elbows was performed to obtain the analysis results. The multi-scale analysis included SHAP analysis, response surface analysis, and Stokes equation analysis.

[0014] As a possible implementation method, the analysis results are:

[0015]

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

[0017] As a possible implementation method, the following method is used to implement SHAP analysis:

[0018]

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

[0020] As a possible implementation method, the response surface analysis is implemented as follows:

[0021]

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

[0023] As a possible implementation method, the following method is used to implement Stokes equation analysis:

[0024]

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

[0026]

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

[0028] As a possible implementation method, the machine learning model is the CatBoost model, and the hyperparameters include: learning rate, depth, and L2 regularization parameter; the hyperparameter optimization machine learning prediction model is specifically as follows:

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

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

[0031] As a possible implementation, S5 uses the following method:

[0032]

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

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

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

[0036] The Lagrangian method is used to track particle trajectories, taking into account drag, gravity, and lift, but ignoring pressure gradient force and virtual mass force, and using the normal e n and tangential e t The rebound model is established using the wall restitution coefficient method;

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

[0038] In a second aspect, the present invention provides a multi-scale series elbow erosion analysis system, comprising:

[0039] A simulation data acquisition unit, configured to acquire n sets of initial data based on a Latin hypercube sampling method, configure a simulation experiment, and obtain n sets of simulation data based on the n sets of initial data;

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

[0041] A series elbow erosion rate prediction unit is used to predict the series elbow erosion rate based on a hyperparameter optimized machine learning prediction model;

[0042] The series elbow erosion analysis unit is used to analyze the factors and influence degree of the erosion rate of series elbows at multiple scales and obtain analysis results. The multi-scale analysis includes: SHAP analysis, response surface analysis and Stokes equation analysis.

[0043] In a third aspect, the present invention provides a terminal comprising a processor and a communication interface coupled to the processor, wherein the processor is configured to execute a computer program or instruction to implement a multi-scale serial bend erosion analysis method provided in the first aspect.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. The multi-scale tandem elbow erosion analysis method proposed in this paper accurately predicts the erosion rate of tandem elbows based on a hyperparameter-optimized machine learning prediction model. SHAP analysis, response surface analysis, and Stokes equation analysis further explain the inherent relationship between the factors affecting the model's erosion rate prediction and the gas-solid erosion prediction of tandem elbows, thereby enhancing the real-time prediction and interpretability of industrial pipeline erosion data.

[0046] 2. The multi-scale series elbow erosion analysis method proposed in this invention analyzes the factors and degree of influence on the erosion rate of series elbows from multiple perspectives. SHAP analysis is used to quantify feature importance (model-driven), response surface analysis is used to reveal interactions (statistically driven), and Stokes equations are used to analyze the physical mechanism (physically driven), thus achieving a full-chain explanation from data to mechanism.

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

[0048] 4. The multi-scale series elbow erosion analysis method proposed in this invention can be extended to more complex pipeline systems (such as multiple elbows and multiphase flow), providing a universal framework for the safe design of industrial pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0050] Figure 1 Flowchart of a multi-scale serial elbow erosion analysis method according to an embodiment of the present invention;

[0051] Figure 2 Schematic diagram of characteristic value distribution of 221 groups of operating parameters in an embodiment of the present invention;

[0052] Figure 3 The following is a comparison of the prediction performance of each model for the average erosion rate of the series elbow wall in the embodiment of the present invention;

[0053] Figure 4 The following is a comparison of the prediction performance of each model for the maximum erosion rate of the upstream elbow in the embodiment of the present invention;

[0054] Figure 5 The following is a comparison of the prediction performance of each model for the maximum erosion rate of the downstream elbow in the embodiment of the present invention;

[0055] Figure 6 The visualization of the prediction of the average erosion rate of the wall surface of the series elbow using the hyperparameter optimized machine learning prediction model in an embodiment of the present invention;

[0056] Figure 7The prediction visualization of the maximum erosion rate of the upstream elbow by the hyperparameter optimized machine learning prediction model in an embodiment of the present invention is shown;

[0057] Figure 8 The following is a visualization of the prediction of the maximum erosion rate of the downstream elbow by the hyperparameter optimized machine learning prediction model in an embodiment of the present invention;

[0058] Figure 9 The prediction of the average erosion rate of the wall of a series elbow pipe by the hyperparameter optimized machine learning prediction model and its confidence interval in the embodiment of the present invention;

[0059] Figure 10 The prediction of the output data and its confidence interval of the hyperparameter optimized machine learning prediction model when predicting the maximum erosion rate of the upstream elbow in an embodiment of the present invention;

[0060] Figure 11 The prediction of the output data and its confidence interval of the hyperparameter optimized machine learning prediction model when predicting the maximum erosion rate of the downstream elbow in an embodiment of the present invention;

[0061] Figure 12 The direction and magnitude of the impact of the five characteristics on the model prediction results when predicting the average erosion rate of the series elbow wall in an embodiment of the present invention;

[0062] Figure 13 The direction and magnitude of the impact of the five characteristics on the model prediction results when predicting the maximum erosion rate of the upstream elbow in an embodiment of the present invention;

[0063] Figure 14 The direction and magnitude of the impact of the five characteristics on the model prediction results when predicting the maximum erosion rate of the downstream elbow in an embodiment of the present invention;

[0064] Figure 15 The figure shows a normal distribution diagram of the residuals of the BBD-RSM model when predicting the average erosion rate of the wall surface of the series elbow in an embodiment of the present invention, and a comparison diagram between the predicted value and the actual value of the BBD-RSM model;

[0065] Figure 16 1. A normal distribution diagram of the residuals of the BBD-RSM model when predicting the maximum erosion rate of the upstream elbow in an embodiment of the present invention, and a comparison diagram between the predicted value and the actual value of the BBD-RSM model;

[0066] Figure 17 1. The figure shows a normal distribution diagram of the residuals of the BBD-RSM model when predicting the maximum erosion rate of the downstream elbow in an embodiment of the present invention, and a comparison diagram between the predicted value and the actual value of the BBD-RSM model;

[0067] Figure 18Schematic diagram of the influence of the other two factors on the maximum erosion rate of the elbow when any two factors of the inner diameter, the ratio of the elbow curvature radius to the elbow distance, the solid particle velocity and the solid particle mass flow rate are fixed in an embodiment of the present invention. DETAILED DESCRIPTION

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

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

[0070] In the present invention, "at least one" refers to one or more, and "more" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent: the existence of A alone, the existence of A and B at the same time, and the existence of B alone, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. The following at least one item (item) or similar expressions thereof refer to any combination of these items, including any combination of single items (items) or plural items (items). For example, at least one item (item) of a, b or c can represent: a, b, c, the combination of a and b, the combination of a and c, the combination of b and c, or the combination of a, b and c, where a, b, c can be single or multiple.

[0071] The embodiments of the present invention aim to provide a multi-scale series elbow erosion analysis method, system and terminal to predict the erosion rate of series elbows with high accuracy, and to analyze the factors and degree of influence of the erosion rate of series elbows at multiple scales, so as to solve the problem that the existing technology is difficult to accurately predict the erosion of gas-dominated solid particle pipelines, and to make up for the current situation that the existing technology has almost no research on the erosion prediction and analysis of series elbows.

[0072] In the first aspect, the present invention provides a multi-scale series elbow erosion analysis method, see Figure 1 , including 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 stratified random process that provides an efficient way to sample variables from a given distribution. The Latin Hypercube Sampling method requires sampling N variables from a specified distribution for each of the k variables X1, X2, ..., Xk. s 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 randomly paired with other variables. Compared to simple random sampling, this special strategy ensures comprehensive coverage of the entire range of each variable by effectively stratifying each marginal distribution to the greatest extent possible.

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

[0076] Table 1 Value range of each factor

[0077] factor symbol unit Value range Elbow distance D mm 152.4～1143 Elbow curvature radius R mm 76.2～381 Elbow inlet velocity V m / s 5～50 Particle size <![CDATA[d0]]> μm 10～500 Relative volume fraction of discrete phase φ ％ 1～10 Total traffic Q kg / s Calculated based on actual model

[0078] After Latin hypercube sampling, 221 groups of operating parameters are obtained, and the value distribution is as follows: Figure 2 As shown in the figure, it can be seen that each variable is evenly valued within the variable range, ensuring the randomness of the data set.

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

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

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

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

[0083]

[0084] Where ρ represents the gas density, represents the velocity vector of the gas, P is the pressure, τ represents the stress tension, represents the body force, represents the additional momentum of the solid particles, μ represents the gas viscosity, I is the unit tensor, and t is the time.

[0085] To accurately simulate turbulent flow, this example uses the Reynolds Stress Model (RSM) as the turbulence model for the simulation experiment, taking into account the diversity of flow directions within the computational domain and the possible secondary flow phenomenon after the elbow. The RSM can more accurately capture the anisotropy and complexity of the flow when the flow direction changes and secondary flow exists. The time-averaged mass conservation and momentum conservation of turbulent incompressible fluid flow are as follows:

[0086]

[0087] Among them, u i represents the average flow velocity, x i represents position, t represents time, p represents average pressure, ρ represents gas density, v represents kinematic viscosity, R ij 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 is the amount of kinetic energy generated by the fluctuation, represents the turbulent (eddy) viscosity, k represents the kinetic energy of the fluctuation, σ k =1, C1=1.8, C2=0.6 are empirical constants, ε represents the turbulent dissipation rate, and the transport equation of the turbulent dissipation rate ε is:

[0091]

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

[0093] After building the turbulence model, the next key step is to select an appropriate near-wall treatment strategy. This example uses an enhanced wall treatment method for near-wall treatment. This method demonstrates greater efficiency than traditional modeling techniques in resolving boundary layer-related issues. The advantage of this enhanced wall treatment method is that it provides more accurate data when simulating flows near walls. Near-wall treatment requires the use of a larger number of boundary layer meshes.

[0094] This embodiment uses the Lagrangian method to track particle trajectories, taking into account drag, gravity, and lift, but ignoring pressure gradient force and virtual mass force, and using the normal e n and tangential e t The rebound model is established using the wall restitution coefficient method;

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

[0096]

[0097] Among them, x p is the particle position, v p is the particle velocity, ρ p is the particle density, μ f is the fluid viscosity, d p is the particle diameter, C D is the resistance coefficient, R ep is the particle Reynolds number, C VM is the imaginary quality factor, which is 0.5 here.

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

[0099]

[0100] Among them, m p is the particle mass, u is the fluid velocity, v p is the particle velocity, Indicates resistance, Represents gravity, F A is the additional force, including the pressure gradient force F P , virtual mass force F VM 、Saffman lift F S .

[0101] These forces, except gravity, are all interphase forces. Among them, resistance plays a dominant role in the movement of particles. Since the density ratio of fluid to particles is very small, the Magnus force and the Basset force can be ignored. In this embodiment, the aspherical drag coefficient is used, and the shape coefficient is 0.8. The drag coefficient C of the spherical particle is D It can be defined as:

[0102]

[0103] Where b1, b2, b3, and b4 are constants based on the particle sphericity (φ) and are used to explain the particle 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 represents the deformation tensor. Only for submicron particles and low Reynolds numbers will the particle motion be significantly affected by the Saffman lift. Therefore, the Saffman lift can be ignored.

[0113] Pressure gradient force F P Expressed as:

[0114]

[0115] Virtual mass force F VM Expressed as:

[0116]

[0117] Where C VM represents the imaginary mass factor, which is only valid when the density ratio When the value is greater than 0.1, the influence of the two forces becomes important. 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 above 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 / 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 pis the particle incident velocity, f(θ) is the incident angle function, θ is the angle between the particle trajectory and the wall, and the pipeline density in this embodiment is 7990 kg / m 3 .

[0122] Next, the boundary conditions were set and the flow simulation was performed in Fluent ANSYS 2022R1, with air (gas) as the carrier fluid. The density and viscosity of air were 1.225 kg / m 3 and 1.789E-05kg / m·s. Select the steady-state flow simulation based on pressure, and gravity acts in the Z direction (-9.81m / s 2 ). The convergence residual is set to less than 10 -3 . The SIMPLE algorithm is selected to couple pressure and velocity, and a second-order scheme is used for the discrete pressure, momentum equation, dissipation rate and turbulent kinetic energy, and a first-order scheme is used for the Reynolds stress equation. The simulation is performed at atmospheric pressure (115.1 kPa). In this embodiment, the inlet boundary and the outlet boundary consider the velocity inlet and pressure outlet conditions respectively, and there is no sliding on the wall. During the simulation process, the flow solution is first obtained, and then the particles are injected into the inlet of the calculation domain. The particles are randomly distributed and the particle velocity is the same as the fluid velocity. The volume concentration value of the particles in this embodiment is very small. Therefore, it is assumed that the effect of the particles on the flow can be ignored, and one-way coupling is used in particle tracking.

[0123] During the erosion process, energy conversion is inevitable when solid particles collide with the pipe wall, and the rebound velocity of the particles will be lower than the incident velocity. This energy conversion is usually 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. In this embodiment, the normal e is used. n and tangential e t The wall restitution coefficient is calculated 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 a possible implementation method, the machine learning model is the CatBoost model, and the hyperparameters include: learning rate, depth, and L2 regularization parameter; the CatBoost model has two major advantages: first, it can automatically process categorical features; second, it can binarize 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 model and the LightBGM model. The main difference is that the CatBoost model can define the tree growth strategy.

[0128] There are two different methods: SymmetricTree and Depthwise. The SymmetricTree growth strategy is to build the tree layer by layer until the specified depth is reached. In each iteration, all leaves from the last tree level are split with the same conditions, and the resulting tree structure is always symmetrical. The Depthwise growth strategy is to build the tree layer by layer until the 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 with the best loss improvement.

[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 growing strategy.

[0130] Since the settings of various model parameters for different data sets will have a great impact on the prediction efficiency, this embodiment adopts a 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, executing the search, selecting the optimal parameters, and retraining the model.

[0131] S4. Train the 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:

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

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

[0134] In order to compare the prediction models, the 221 data sets were divided into training and test sets in a ratio of 8:2. The random forest model (RF), LightBGM model, AdaBoost model, XGBoost model, and CatBoost model were constructed after grid search hyperparameter tuning to determine the coefficient (R 2 ), root mean square error (RMSE) and mean absolute error (MAE) are used to evaluate the superior performance of the CatBoost model used in the embodiment of the present invention compared with other models. The model output is the maximum erosion rate in kg / m 2 s. For comparison, see Figures 3 to 5 , Figure 3 The performance of each model for predicting the average wall erosion rate of a series elbow is shown. The CatBoost model achieves 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 (CDR) reaches 0.99, the highest, indicating that this model predicts nearly all of the data and performs best. The LightBGM and AdaBoost models have lower CDRs, around 0.92, indicating weaker fitting capabilities. Figure 4 The performance of each model for predicting the maximum erosion rate of the upstream elbow is demonstrated. The CatBoost model once again performed well, with a root mean square error of 1.67e-01 and a mean absolute error of 1.03e-01. It also achieved the highest coefficient of determination for this task, reaching 0.95, indicating its superior performance in predicting the maximum erosion rate of the upstream elbow. The LightBGM model had the lowest coefficient of determination, only 0.79, reflecting its weaker fitting ability for this task. The AdaBoost model also had a relatively large error, with a root mean square error of nearly 4.30e-01. Other models, such as the XGBoost model, had coefficients of determination around 0.88, indicating moderate performance. Figure 5 The prediction performance of each model for the maximum erosion rate of the downstream elbow is demonstrated. In this task, the CatBoost model's optimization model and the random forest model had the lowest errors, with root mean square errors of 2.64e-01 and 2.62e-01, respectively. The random forest model achieved an excellent performance with a coefficient of determination of 0.90; the CatBoost model's optimization model had a slightly lower coefficient of determination of 0.89, but also outperformed the other models. The AdaBoost model had the lowest coefficient of determination in this task, at only 0.70, indicating that its fitting effect in this scenario was poor. The errors of the LightBGM model and the XGBoost model were also relatively high, especially the LightBGM model, which had a root mean square error of 3.49e-01.

[0135] In summary, the CatBoost model of the embodiment of the present invention performs well in all tasks, especially in the prediction performance of the average erosion rate of the wall surface of the series elbow, with the lowest error and the highest determination coefficient value.

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

[0137] As a possible implementation, S5 uses the following method:

[0138]

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

[0140] See also Figures 6 to 8 , in order to optimize the accuracy of the regression prediction of the machine learning prediction model for three tasks, the three tasks are: Task 1: Prediction of the average erosion rate of the wall of the series elbow; Task 2: Prediction of the maximum erosion rate of the upstream elbow; Task 3: Prediction of the maximum erosion rate of the downstream elbow. Figures 9 to 11 The figure shows the predictions and confidence intervals for the output data of a hyperparameter-optimized machine learning prediction model for 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 in the figure represent the test data, which are the actual observations of the model. These data points provide a benchmark for the model's predictions, making it easier to evaluate the model's performance. The dark blue curve represents the mean prediction μ of the hyperparameter-optimized machine learning prediction model. This curve shows the model's prediction results for each test sample, and comparison with the red data points can help observe the model's goodness of fit. The confidence intervals in the figure, shades of blue, provide a quantitative representation of the uncertainty of the model's predictions. Overall, the figure shows how well the hyperparameter-optimized machine learning prediction model fits the data. Most of the predictions are close to the actual data, while also capturing significant fluctuations.

[0141] S6. Multi-scale analysis of the factors and degree of influence on the erosion rate of the series elbow was performed to obtain the analysis results. The multi-scale analysis included SHAP analysis, response surface analysis, and Stokes equation analysis. The analysis results were as follows:

[0142]

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

[0144] As a possible implementation method, the following method is used to implement SHAP analysis:

[0145]

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

[0147] As an example, the SHAP value can be calculated by considering the marginal contributions of the eigenvalues 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 may be related to erosion. Next, the SHAP value is used to evaluate the contribution of each eigenvalue to the erosion rate. This example uses the SHAP library in Python to calculate the SHAP value, see Figures 12 to 14 , respectively, are the effects of five features (total flow Q, elbow inlet velocity V, particle size d0, elbow curvature radius 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 figure represents the SHAP value, which shows the direction and magnitude of the feature's influence on the model prediction results. A positive SHAP value indicates that the feature has a positive impact on the model output, while a negative one indicates the opposite. Figures 12 to 14 In the figure, features Q and V have the most significant impact on the model output. Their SHAP values are widely distributed, indicating a significant contribution to the prediction. High values of feature Q (red) generally increase the model output, while low values (blue) decrease it. High values of feature V have a similar positive impact, while low values decrease the model prediction. Figure 12 and Figure 13 The influence of feature d0 is relatively small, with a narrow range of SHAP values, indicating that its impact on the model output is limited. Features R and D have an even weaker impact, with almost no significant positive or negative impact on the model output, but low and high values still have some small effect on the model predictions. The color gradient in the legend represents the magnitude of each feature, with high values in red and low values in blue. Overall, the relationship between color and SHAP value indicates that increasing feature values can lead to positive or negative changes in the SHAP value, which in turn affects the model predictions.

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

[0149] First, analyzing the flow state changes, we can see that in a series elbow system, the gas-solid fluid undergoes significant flow state changes when passing through the elbow. At the upstream elbow, due to the relatively uniform mixing of the fluids, the elbow inlet velocity V contributes significantly to the erosion rate. However, after passing through the upstream elbow, the flow field changes, and the flow characteristics of the solid particles also change accordingly. At this point, the impact of the particles on the wall may be more significant, causing the SHAP value of the particle size d0 at the downstream elbow to exceed the SHAP value of the elbow inlet velocity V.

[0150] Second, considering the differences in erosion mechanisms, particles of different sizes can trigger different forms of erosion during gas-solid two-phase flow erosion. At the upstream elbow, the elbow inlet velocity, V, dominates the erosion rate; at the downstream elbow, the velocity influence is reduced. The reduced velocity weakens the effect of large particles, leaving small particles more susceptible to wall erosion, causing the influence of particle size d0 to exceed the elbow inlet velocity, V.

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

[0152] Fourth, from the perspective of feature interaction effects, significant interactions may exist between different features at different elbow locations. For upstream elbows, erosion is more dependent on inlet velocity, and the interaction between elbow inlet velocity V and particle size d0 is relatively small. However, at downstream elbows, the effect of elbow inlet velocity V is weakened, making the contribution of particle size more significant. In addition, this may be because the interaction between particle size and other features (such as elbow inlet velocity V and elbow curvature radius R) is more significant at this location.

[0153] As a possible implementation method, the response surface analysis is implemented using the following method:

[0154]

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

[0156] As an example, the response surface analysis strategy adopted in the present embodiment is response surface (Box-Behnken, BBD) design, and the processing combination of BBD is located at the center point of the edge of the test space, requiring at least three factors, and each factor has only three levels to ensure that all factors are not set at a high level at the same time. Response surface design can be used to evaluate the nonlinear effects of factors and first-order and second-order coefficients. Combining the single-action analysis results and the actual engineering situation of the gas-solid series elbow, particle size, elbow distance, elbow curvature radius, elbow inlet velocity, and total flow are selected as the factors of Box-Behnken design-response surface model (Box-Behnkendesign-response surface method, BBD-RSM). The factors and level settings of the BBD-RSM model are shown in Table 1:

[0157] Table 1 Factor and level settings of 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 variance analysis is shown in Table 3:

[0165] Table 3 Variance analysis results of each index

[0166]

[0167]

[0168] A P value less than 0.0500 indicates that the model term is significant. As can be seen in Table 3, in Tasks 1 to 3, the P value of the BBD-RSM model designed in the embodiment of the present invention is less than 0.0001, indicating that the model has extremely significant and good adaptability.

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

[0170] See also Figures 15 to 17 , the residual normal distribution diagram of the BBD-RSM model in the three tasks and the comparison diagram of the predicted value and the actual value of the BBD-RSM model, Figure 15 (a) Figure 16 (a) and Figure 17 (a) shows that the residual values of the BBD-RSM model in the three tasks are linear and evenly distributed, indicating that the model is adaptive; Figure 15 (b) Figure 16 (b) and Figure 17 (b) shows that the BBD-RSM model has higher prediction accuracy in the three tasks.

[0171] See also Figure 18 , shows the influence of the other two factors on the maximum erosion rate of the elbow when any two factors of inner diameter, R / D ratio, solid particle velocity and solid particle 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 map formed by the projection of the response surface on the bottom surface can reflect the interaction between the factors, that is, the elliptical contour line indicates that the interaction between the factors is obvious, while the straight line indicates that the interaction between the factors is not obvious. For the upstream elbow, Figure 18 In (a), we can see the significant effect of the interaction between particle diameter and gas-solid velocity on the erosion rate. Larger particles have a greater impact on the pipe wall at high velocities, resulting in a higher erosion rate. In addition, the synergistic effect between particle diameter and flow velocity causes the erosion rate to increase rapidly. Figure 18 In (b), the interaction between particle diameter and solid particle flow rate on the maximum erosion rate is also very obvious. 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, the higher solid particle flow rate significantly increases the erosion rate. This interaction shows that when large particles and high flow rates are present at the same time, the erosion risk increases sharply. Figure 18In (c), we can see the effect of the interaction between gas-solid velocity and particle flow rate on the erosion rate. High velocity increases the kinetic energy of the particles, while high flow rate means more particles will hit the pipe wall. The synergistic effect of these two factors leads to higher impact frequency and impact force, which intensifies erosion. For the downstream bend, Figure 18 In (d), we can see that as the particle size increases, the erosion rate shows a gradually increasing trend, especially when the elbow radius is small, the erosion is more serious. Figure 18 In (e), it can be seen that the interaction between gas-solid velocity and particle size has no significant effect on the erosion rate of the downstream elbow. Figure 18 In (a), the interaction between gas-solid velocity and particle size has a greater impact on the upstream elbow erosion rate, but the trends are similar. Figure 18 The performance of (f) and Figure 18 Similar to (c).

[0172] Through interaction analysis, the embodiments of the present invention can better understand how these factors jointly affect the pipeline erosion rate, thereby providing more accurate operation guidance and equipment design solutions.

[0173] As a possible implementation method, the following method is used to implement Stokes equation analysis:

[0174]

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

[0176]

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

[0178] As an example, the gas has different acceleration characteristics for particles of different sizes, resulting in different particle velocities and ultimately different erosion rates. The Stokes number represents the ratio of the relaxation time of solid particles to the characteristic time of the fluid. It reflects the correlation between the inertial force and resistance of solid particles. In addition, it is a dimensionless number that reflects the curved motion of particles. When the Stokes number is less than 1, the particles can easily follow the movement of the surrounding fluid. When the Stokes number is much greater than 1, the influence of the fluid on the particle motion becomes smaller. Next, two typical working conditions, working conditions A and working conditions B, are used as examples for explanation. The Stokes numbers of working conditions A and B are shown in Table 4:

[0179] Table 4 Stokes numbers of working conditions A and B

[0180]

[0181]

[0182] The Stokes number for Condition A is 1.11. As particle size increases, the Stokes number increases, reaching 194.18 for Condition B, which is significantly greater than 1. This indicates that under Condition B, the gas cannot easily carry solid particles. Combined with Facet Maximum-all statistical numerical analysis, it can be seen that at the upstream bend, large particles cause a higher erosion rate than small particles. This is because particles of different sizes enter at the same velocity, but large particles collide with the wall with greater kinetic energy. Therefore, larger particles cause greater damage at the upstream bend. The opposite is true at the downstream bend, where large particles cause less erosion. Large particles collide and lose kinetic energy at the upstream bend, and due to the high Stokes number, the gas has poor mobility for large particles. Therefore, at the downstream bend, erosion caused by large particles is less. Therefore, the small-sized particles in working condition A can be accelerated by the gas and cause greater damage to the downstream elbow than the large-sized particles in working condition B. Among the factors affecting the maximum erosion rate at the downstream elbow, the effect of particle size will be more obvious than that at the upstream elbow.

[0183] The following is an example to illustrate the practical application of this solution:

[0184] Example 1 (small particles dominate downstream erosion):

[0185] (1) Specific working conditions:

[0186] Elbow distance: 572.75mm

[0187] Elbow radius: 364.19mm

[0188] Inlet velocity: 25.56m / s

[0189] Particle size: 11.58 μm

[0190] Total flow rate: 18.81 kg / s

[0191] Stokes number: 1.11 (Stk≈1, particles tend to move with the airflow).

[0192] (2) SHAP analysis:

[0193] Upstream elbow (p1): The SHAP values of gas-solid velocity (V) and total flow (Q) are the highest (V: +0.85, Q: +0.78), indicating that high-speed airflow and high flow jointly drive erosion;

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

[0195] (3) Response surface analysis

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

[0197] Contour shape: The elliptical contour indicates 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 fully follow the airflow, briefly impact the upstream bend due to high velocity, and enhance erosion in the downstream bend due to the cumulative effect;

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

[0201] Example 2 (large particles dominate upstream erosion):

[0202] (1) Specific working conditions:

[0203] Elbow distance: 558.77mm

[0204] Elbow radius: 333.11mm

[0205] Inlet velocity: 35.81m / s

[0206] Particle size: 129.08 μm

[0207] Total flow rate: 14.04 kg / s

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

[0209] (2) SHAP analysis:

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

[0211] Downstream elbow (p2): The SHAP value of the total flow (Q) decreases (+0.43) because the large particles lose kinetic energy in the upstream elbow and their impact on the downstream elbow is weakened.

[0212] (3) Response surface analysis

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

[0214] (4) Stokes equation analysis:

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

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

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

[0218] (1) Specific working conditions:

[0219] Elbow distance: 647.70mm

[0220] Elbow radius: 228.60mm

[0221] Entrance velocity: 27.50m / s

[0222] Particle size: 255.00 μm

[0223] Total flow rate: 25.50kg / s

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

[0225] (2) SHAP analysis:

[0226] Upstream elbow (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 elbow (p2): The SHAP value of the elbow radius (R) is significantly negative (-0.55), indicating that the smaller radius leads to turbulent flow field at the downstream elbow and aggravated erosion.

[0228] (3) Response surface analysis

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

[0230] Contour shape: dense ellipse indicates that the interaction between R and V has a significant effect on the downstream elbow erosion (R 2 =0.85).

[0231] (4) Stokes equation analysis:

[0232] Particle behavior: Stk = 87.45 (>1), the particle partially escapes from the airflow trajectory, causing moderate impact at the upstream bend due to the medium velocity, and at the downstream bend due to the small elbow radius, the secondary flow is enhanced and the erosion distribution is diffused;

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

[0234] The multi-scale series elbow erosion analysis method proposed in this embodiment and the CatBoost model can predict the erosion rate of series elbows with high accuracy. Through SHAP analysis, response surface analysis and Stokes equation analysis, the intrinsic connection between the influence of model erosion rate prediction and the influence of series elbow gas-solid erosion prediction can be further explained, thereby increasing the real-time prediction capability and interpretability of industrial pipeline erosion data.

[0235] In a second aspect, the present invention provides a multi-scale series elbow erosion analysis system, comprising:

[0236] A simulation data acquisition unit, configured to acquire n sets of initial data based on a Latin hypercube sampling method, configure a simulation experiment, and obtain n sets of simulation data based on the n sets of initial data;

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

[0238] A series elbow erosion rate prediction unit is used to predict the series elbow erosion rate based on a hyperparameter optimized machine learning prediction model;

[0239] The series elbow erosion analysis unit is used to analyze the factors and influence degree of the erosion rate of series elbows at multiple scales and obtain analysis results. The multi-scale analysis includes: SHAP analysis, response surface analysis and Stokes equation analysis.

[0240] In a third aspect, the present invention provides a terminal comprising a processor and a communication interface coupled to the processor, wherein the processor is configured to execute a computer program or instruction to implement the multi-scale serial bend erosion analysis method provided in the first aspect.

[0241] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the drawings, the disclosure, and the accompanying drawings. In the specification, the word "comprising" does not exclude other components or steps, and "one" or "an" does not exclude multiple situations. A single processor or other unit can implement several functions listed in the specification. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0242] Although the present invention has been described with reference to specific features and embodiments thereof, it will be apparent that various modifications and combinations thereof may be made without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the present invention and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the invention. It will be apparent that various modifications and variations of the present invention may be made by those skilled in the art without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such modifications and variations as fall within the scope of the invention and its equivalents.

Claims

1. A multi-scale erosion analysis method for series elbows, characterized in that: The steps include: S1. Obtain n sets of initial data based on the Latin hypercube sampling method; S2. Configure a simulation experiment to obtain n sets of simulation data based on the n sets of initial data; S3. Select a machine learning model and optimize its hyperparameters using a grid search method. S4. Training the machine learning model based on the simulation data to obtain a hyperparameter optimized machine learning prediction model; S5. Predicting the erosion rate of the series elbow based on the hyperparameter optimized machine learning prediction model; S6. Multi-scale analysis of factors affecting the erosion rate of the series elbow and the degree of influence to obtain analysis results, wherein the multi-scale analysis includes: SHAP analysis, response surface analysis and Stokes equation analysis.

2. The multi-scale tandem elbow erosion analysis method according to claim 1, characterized in that: The analysis results are: in, represents the SHAP analysis results, It represents the degree of interaction between any two factors, and Effect (d0→pi) represents the degree of influence of particle size on the upstream elbow or downstream elbow.

3. The multi-scale tandem elbow erosion analysis method according to claim 2, characterized in that: The SHAP analysis is implemented as follows: Where i∈{1,2}, p1 represents the upstream elbow, p2 represents the downstream elbow, represents the SHAP analysis result, φ(M) is the SHAP value calculation function based on the hyperparameter optimization machine learning prediction model, D represents the elbow distance, R represents the elbow curvature radius, V represents the elbow inlet velocity, d0 represents the particle size, Q represents the total flow rate, j represents the jth group of simulation data, 1≤j≤n, and n represents the nth group of simulation data.

4. The multi-scale tandem elbow erosion analysis method according to claim 2, characterized in that: The response surface analysis was performed using the following method: Where i∈{1,2}, p1 represents the upstream elbow, p2 represents the downstream elbow, x, y∈(D,R,V,d0,Q) and x≠y, D represents the elbow distance, R represents the elbow curvature radius, V represents the elbow inlet velocity, d0 represents the particle size, Q represents the total flow rate, It represents the degree of interaction between any two factors, and RSM represents response surface analysis.

5. The multi-scale tandem elbow erosion analysis method according to claim 2, characterized in that: The Stokes equation analysis is implemented as follows: Among them, ρ p represents the particle density, d p represents the particle diameter, u represents the fluid velocity, μ represents the fluid dynamic viscosity, and D represents the pipe diameter. The degree of influence of particle size on the upstream or downstream elbow is as follows: Among them, Effect (d0→p1) represents the influence of particle size on the upstream elbow, and Effect (d0→p2) represents the influence of particle size on the downstream elbow.

6. The multi-scale tandem elbow 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 machine learning prediction model is specifically: M=CatBoost[D Train ,i * (a,b,c)] Among them, D Train represents the training set in n sets of simulation data, θ * represents the optimal parameters, (a, b, c) represents the CV parameter search space, and the CV parameters are k∈{1,2,3,4,5}.

7. The multi-scale tandem elbow erosion analysis method according to claim 6, characterized in that: The S5 is implemented by the following method: in, represents the predicted value of the erosion rate of the series elbow, D represents the elbow distance, R represents the elbow curvature radius, V represents the elbow inlet velocity, d0 represents the particle size, Q represents the total flow rate, and M represents the hyperparameter optimization machine learning prediction model.

8. The multi-scale tandem elbow erosion analysis method according to claim 1, characterized in that: The simulation experiment includes fluid flow modeling and particle trajectory tracking; The fluid flow modeling includes: considering gas as a continuous phase, using the Reynolds stress model as a turbulence model, and adopting an enhanced wall processing method for near-wall processing; The Lagrangian method is used to track particle trajectories, taking into account drag, gravity, and lift, but ignoring pressure gradient force and virtual mass force, and using the normal e n and tangential e t The rebound model is established using the wall restitution coefficient method; The Finnie erosion model is used as the erosion model.

9. A multi-scale series elbow erosion analysis system, characterized in that: include: A simulation data acquisition unit, configured to acquire n sets of initial data based on a Latin hypercube sampling method, configure a simulation experiment, and obtain n sets of simulation data based on the n sets of initial data; A 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 a grid search method, train the machine learning model based on simulation data, and obtain a hyperparameter optimized machine learning prediction model; A series elbow erosion rate prediction unit, configured to predict the series elbow erosion rate based on the hyperparameter optimized machine learning prediction model; The series elbow erosion analysis unit is used to analyze the factors and influence degree of the erosion rate of series elbows at multiple scales and obtain analysis results. The multi-scale analysis includes: SHAP analysis, response surface analysis and Stokes equation analysis.

10. A terminal comprising a processor and a communication interface coupled to the processor, wherein the processor is configured to execute a computer program or instruction to implement the multi-scale serial elbow erosion analysis method according to any one of claims 1 to 8.

Images