A method for predicting corrosion rate in oil and gas pipelines based on IWOA-SVM

By combining whale optimization algorithm and support vector machine, a corrosion rate prediction model in oil and gas pipelines is established, which solves the problem of difficulty in accurately predicting corrosion rates in oil and gas pipelines in the prior art, achieving high-precision prediction and improving the safety of pipeline operations.

CN118332922BActive Publication Date: 2025-03-04SOUTHWEST PETROLEUM UNIV
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Patent Information

Application Number
CN202410549000.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-05-06
Publication Date
2025-03-04
Estimated Expiration
2044-05-06

AI Technical Summary

Technical Problem

The prior art is difficult to accurately predict the corrosion rate in oil and gas pipelines, resulting in the safety of pipeline operations being threatened.

Method used

A combination of whale optimization algorithm (IWOA) and support vector machine (SVM) is used to establish a corrosion rate prediction model in oil and gas pipelines. This method improves prediction accuracy by introducing adaptive weights and nonlinear convergence factors.

Benefits of technology

High-precision prediction of corrosion rates in oil and gas pipelines is achieved, and the safety and reliability of pipeline operations are improved.

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Abstract

The present invention discloses a method for predicting the internal corrosion rate of oil and gas pipelines based on IWOA-SVM, comprising the following steps: S1. Selecting factors that are representative and relevant to the internal corrosion behavior during the operation of the oil and gas pipeline as input variables; S2. Preprocessing the input variables and organizing the processed data into a data set; S3. Dividing the data in the data set into a training set and a test set; S4. Establishing an oil and gas pipeline corrosion rate prediction model based on IWOA-SVM, and predicting the internal corrosion rate. The present invention improves the traditional whale method and combines it with the SVM method. The improvement includes introducing adaptive weights and nonlinear convergence factors, balancing global search and local development capabilities, so that it has both strong global search capabilities and is not easy to fall into local optimal solutions.
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Description

Technical Field

[0001] The invention relates to the technical field of oil and gas pipeline transportation, and in particular to an IWOA-SVM-based method for predicting corrosion rate in oil and gas pipelines. Background Art

[0002] Pipeline transportation is regarded as the safest and cost-effective way to transport long-distance and large-volume fluids. With the rapid development of the oil and gas industry, thousands of kilometers of pipelines have been installed in various water depths and soil conditions around the world. The vast pipeline network is vital to the global economy. However, pipelines are susceptible to various damages and aging defects. Thousands of accidents have proven that the consequences of pipeline failures are catastrophic in both economic and environmental terms. Therefore, ensuring the safety of pipeline operations is essential to the world's energy needs. Many studies have shown that internal corrosion occupies a prominent position in the risk assessment of oil and gas transportation pipelines. By predicting the internal corrosion of oil and gas pipelines, pipeline operators can reasonably implement pipeline management, inspection and preventive maintenance. Therefore, in the field of pipeline risk assessment, the prediction of internal corrosion of oil and gas pipelines is the focus of industry attention, and many researchers are committed to seeking effective and accurate prediction methods.

[0003] The whale optimization algorithm (IWOA) is a new type of swarm intelligence optimization algorithm in the field of swarm intelligence algorithms, in addition to the ant colony algorithm and particle swarm algorithm. This algorithm is a new swarm intelligence optimization algorithm proposed by Mirjalili et al. from Griffith University, Australia in 2016. In the whale optimization algorithm, each whale represents a solution. The whales continuously explore and hunt prey during the iteration of the algorithm, and constantly try to improve their solutions. The whale optimization algorithm can effectively solve various complex optimization problems and has a fast convergence speed. Since its invention, the whale optimization algorithm has been widely used in industry and academia, and has received increasing attention in recent years. At present, the whale optimization algorithm has become a popular optimization algorithm and has been widely used in many research fields. The whale optimization algorithm is a simulation algorithm based on whale behavior, which is used to solve optimization problems. It simulates the hunting behavior of humpback whale groups in nature, and achieves the purpose of optimal search through the process of whale group searching, encircling, chasing and attacking prey.

[0004] Given the many uncertainties in the field of internal corrosion prediction for oil and gas pipelines, it is challenging to determine the law of defect development under actual working conditions. Therefore, corrosion rate prediction is quite difficult. Therefore, it is imperative to explore new methods to improve the accuracy of internal corrosion rate prediction. Summary of the invention

[0005] In order to solve the above problems, the present invention provides a method for predicting the internal corrosion rate of oil and gas pipelines based on IWOA-SVM, comprising the following steps: S1. selecting factors that are representative and relevant to the internal corrosion behavior during the operation of the oil and gas pipeline as input variables; S2. preprocessing the input variables and organizing the processed data into a data set; S3. dividing the data in the data set into a training set and a test set; S4. establishing an oil and gas pipeline corrosion rate prediction model based on IWOA-SVM, and predicting the internal corrosion rate.

[0006] Furthermore, the factors that are representative and relevant to the internal corrosion behavior in step S1 specifically include: CO2 partial pressure, CO2 concentration, temperature, pH value, medium flow rate, Cl - concentration.

[0007] Furthermore, the specific step of preprocessing the input variables in step S2 is: normalizing the data, wherein the calculation formula for data normalization is: In the formula, X is the input variable vector, X min is the minimum value of the input variable vector, X max is the maximum value of the input variable vector, and X' is the normalized input variable vector.

[0008] Furthermore, the establishment of the oil and gas pipeline corrosion rate prediction model based on IWOA-SVM in step S4 specifically includes the following sub-steps: S41. Using SVM as the basic model of the corrosion rate in the oil and gas pipeline; S42. Improving the IWOA method; S43. Using the improved IWOA method to optimize the SVM.

[0009] Furthermore, the step S41 specifically includes the following sub-steps: S411. Setting the total number of samples and determining the input-output relationship model; S412. Establishing constraints to optimize the input-output relationship model; S413. Introducing a kernel function and classifying and mapping the samples.

[0010] Furthermore, the IWOA method is improved in step S42, and the calculation method of the convergence factor a, the local search update method X(t+1) and the weight ω(t) in the IWOA method are improved. The specific improvements are as follows: The calculation formula of the optimized convergence factor a is: In the formula, a ini with a fin is the initial and final value of the convergence factor, t is the current iteration number, T max is the maximum number of iterations; the linearly changing inertia weight is changed into the nonlinearly changing adaptive weight, and the calculation formula of the local search update X(t+1) after the change is: Where ω(t) is the adaptive weight that changes with the number of iterations t, is the rate at which the inertia weight changes dynamically with the number of iterations, is the current optimal individual position, X(t) is the current individual position, A is the coefficient vector, D is the distance between the current individual position and the optimal individual position, b is the spiral shape constant, l is a random number between [-1,1], and p is a random number between [0,1]; the calculation formula of the adaptive weight ω(t) is: In the formula, ω max ,ω min are the maximum and minimum values ​​of the inertia weight respectively.

[0011] Furthermore, the calculation formula of ω(t) in step A5 is: In the formula, ω max ,ω min are the maximum and minimum values ​​of the inertia weight respectively.

[0012] Furthermore, the specific implementation steps of step S43 include: B1. Initializing the parameter weights and thresholds of SVM and initializing IWOA; B2. Setting the population size N of humpback whales and the maximum number of iterations T max , iteration number t = 0, use the kernel parameter g and penalty factor C of SVM as the position vector of IWOA; B3. Update the nonlinear convergence factor and adaptive weight, calculate the coefficient vector A, and initialize the random numbers p, l; B4. Update the humpback whale position information according to the value of A; B5. Determine whether the number of iterations reaches the maximum number of iterations; B6. Output the optimal solution and obtain the optimal kernel parameter g and the optimal penalty factor C.

[0013] Furthermore, the step B5 specifically includes the following sub-steps: when the iteration number reaches the maximum iteration number, execute step B6; when the iteration number does not reach the maximum iteration number, add 1 to the current iteration number and repeat step B3.

[0014] Furthermore, the method further includes the step of evaluating the prediction results: S5. Evaluating the prediction results according to relevant evaluation indicators; wherein the relevant evaluation indicators specifically include: mean absolute error MAPE, root mean square error RMSE, determination coefficient R 2 .

[0015] Furthermore, the calculation formula of the mean absolute error MAPE is:

[0016] The calculation formula of root mean square error RMSE is:

[0017] Coefficient of determination R 2 The calculation formula is:

[0018] In the above formula, n is the number of samples, y is the actual value, is the predicted value, is the average of the actual numbers.

[0019] The present invention provides a method for predicting the corrosion rate in oil and gas pipes based on IWOA-SVM, which has the following beneficial effects:

[0020] The present invention improves the traditional whale method and combines it with the SVM method to propose the IWOA-SVM method. The improvements include introducing adaptive weights and nonlinear convergence factors, balancing global search and local development capabilities, so that it has both strong global search capabilities and is not easy to fall into local optimal solutions. The present invention combines the improved WOA model with the SVM method to achieve high-precision prediction of corrosion in in-service oil and gas pipelines and ensure the safety of in-service oil and gas pipeline operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0022] Figure 1 A flow chart of the method provided by the present invention;

[0023] Figure 2 The actual value of the corrosion rate in the oil and gas pipeline in the simulation experiment provided by the present invention and the predicted value of each SVM model. DETAILED DESCRIPTION

[0024] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0025] The following is a detailed description of the implementation method of the present invention in conjunction with the accompanying drawings. Only some embodiments are described, not all embodiments. For the purpose of clarity, representations and descriptions that are not related to the present invention are omitted in the drawings and descriptions.

[0026] In order to have a clearer understanding of the technical features, purposes and beneficial effects of the present invention, the technical solution of the present invention is now described in detail below. Obviously, the implementation cases described are part of the embodiments of the present invention, not all of the embodiments, and cannot be understood as limiting the scope of the implementation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0027] like Figure 1 As shown, the present invention provides an oil and gas pipeline internal corrosion rate prediction method based on IWOA-SVM, comprising the following steps: S1. Selecting factors that are representative and relevant to the internal corrosion behavior during the operation of the oil and gas pipeline as input variables; S2. Preprocessing the input variables, and organizing the processed data into a data set; S3. Dividing the data in the data set into a training set and a test set; S4. Establishing an oil and gas pipeline corrosion rate prediction model based on IWOA-SVM, and predicting the internal corrosion rate.

[0028] Among them, the factors that are representative and relevant to the internal corrosion behavior in step S1 include: CO2 partial pressure, CO2 concentration, temperature, pH value, medium flow rate, Cl - concentration.

[0029] The specific steps of preprocessing the input variables in step S2 are: normalizing the data, where the calculation formula for data normalization is: In the formula, X is the input variable vector, X min is the minimum value of the input variable vector, X max is the maximum value of the input variable vector, and X' is the normalized input variable vector.

[0030] The oil and gas pipeline corrosion rate prediction model based on IWOA-SVM established in step S4 specifically includes the following sub-steps: S41. Using SVM as the basic model of corrosion rate in oil and gas pipelines; S42. Improving the IWOA method; S43. Using the improved IWOA method to optimize the SVM model.

[0031] Among them, step S41 specifically includes the following sub-steps: S411. Set the total number of samples and determine the input-output relationship model; S412. Establish constraints to optimize the input-output relationship model; S413. Introduce kernel functions and classify and map samples.

[0032] Use SVM as the basic model of corrosion rate in oil and gas pipelines: The basic idea of ​​SVM is to separate data points of different categories by finding an optimal hyperplane, while ensuring that this separation hyperplane has the largest interval among all possible separation hyperplanes. The method idea of ​​SVM is described as follows:

[0033] The t input variables for the i-th sample are represented by a vector: i =[x i (1), x i (2), …, x i (t)]; and the output variable corresponding to the i-th sample is represented by yi.

[0034] Assuming there are N samples in total, the relationship between input and output can be expressed as follows: In the formula, w is the weight coefficient vector, (x i ) is the mapping from input space to high-dimensional space, and b represents the bias.

[0035] To obtain a more precise expression, the optimization objective can be determined under the following constraints: In the formula, ζ and ζ * is the slack variable, and ε is the insensitivity, i.e. the error tolerance range. The optimization goal is: Where C is the penalty factor, which indicates the degree of penalty for samples when the insensitivity ε is exceeded, and is used to balance the accuracy and complexity of the model.

[0036] By constructing the Lagrangian function and introducing the kernel function K(xi, xj): In the formula, α i With α i * is the Lagrange coefficient, K(x i , x j ) is the kernel function. When SVM is used to classify corrosion data samples, SVM maps the samples to a high-dimensional space using the kernel function.

[0037] Select RBF as the SVM kernel function, and the kernel function expression is: K(x i , x j )=exp(-g||F i -F j || 2 ) g<0; where exp is the exponential function, g is the kernel parameter in the RBF kernel function, and the kernel parameter g and the penalty factor C jointly determine the SVM classification effect.

[0038] The specific implementation steps of step S42 include:

[0039] A1. Surrounding the target prey: The position of the humpback whale closest to the prey is the optimal solution. The remaining humpback whales gradually update their positions with the goal of moving closer to the optimal solution. The calculation formula is:

[0040]

[0041] In the formula, is the current optimal solution humpback whale position, X(t) is the current humpback whale position, t is the current iteration number, A and C are coefficient vectors, r1 and r2 are random vectors between [0,1], D is the distance between the current humpback whale position and the optimal solution position, and a is the convergence factor that decreases linearly from 2 to 0 during the iteration process.

[0042] A2. Spiral bubble net attack: The humpback whale updates its position by shrinking, surrounding and spiraling, gradually approaching its prey and finally launching an attack. The calculation formula for the humpback whale's spiral movement is:

[0043]

[0044] Where b is a spiral shape constant and l is a random number between [-1,1].

[0045] The spiral position is updated or the shrinkage is judged based on the p value, and the calculation formula is:

[0046]

[0047] Where p is a random number between [0,1].

[0048] A3. Searching and locking the target prey: Humpback whales can not only track prey through the spiral bubble net method, but also search for prey through the positions of humpback whales. When the coefficient vector |A|≥1, the humpback whale updates the position based on the optimal solution humpback whale position and changes it to the randomly selected humpback whale position, and then performs global optimization; when the coefficient vector |A|<1, the humpback whale still updates the position with the optimal solution position and performs local optimization. The calculation formula is:

[0049]

[0050] In the formula, X rand (t) is the position of a random whale.

[0051] The IWOA method is simple in principle and requires few parameters to be adjusted manually. However, the optimization ability of the method is entirely determined by the convergence factor a. The smaller the value of a, the more inclined the method is to local optimization; the larger the value of a, the closer the method is to global optimization. The value of a changes linearly, which may cause the method to be trapped in local optimization. Therefore, the introduction of nonlinear adjustment can improve the method's search ability without changing the decreasing trend of a.

[0052] A4. Optimize the convergence factor a. The calculation formula of the optimized convergence factor a is:

[0053]

[0054] In the formula, a ini with a fin are the initial and final values ​​of the convergence factor, and t is the number of iterations.

[0055] When the nonlinear convergence factor is introduced, the linearly changing inertia weight cannot make the method have a better optimization effect.

[0056] A5. The linearly changing inertia weight is changed into the nonlinearly changing adaptive weight. The calculation formula after the change is:

[0057]

[0058] Where ω(t) is the adaptive weight that changes with the number of iterations t, is the rate at which the inertia weight changes dynamically with the number of iterations.

[0059] Among them, the calculation formula of ω(t) in step A5 is: In the formula, ω max ,ω min are the maximum and minimum values ​​of the inertia weight respectively.

[0060] The specific implementation steps of step S43 include:

[0061] B1. Initialize the parameter weights and thresholds of SVM and initialize IWOA.

[0062] B2. Set the population size of humpback whales N and the maximum number of iterations T max , the iteration number t = 0, the kernel parameter g of SVM and the penalty factor C are used as the position vector of IWOA.

[0063] B3. Update the nonlinear convergence factor and adaptive weight, calculate the coefficient vector A, and initialize the random numbers p and l. The formula updates the nonlinear convergence factor a according to The formula updates the adaptive weights and substitutes the nonlinear convergence factor a into The coefficient vector A is calculated in the formula.

[0064] B4. Update the humpback whale location information based on the A value.

[0065] When |A|≥1, according to In the formula, when p<0.5, the position information is updated; when |A|<1, the position information is updated according to Update location information.

[0066] B5. Determine whether the number of iterations has reached the maximum number of iterations: When the number of iterations has reached the maximum number of iterations, execute step B6; when the number of iterations has not reached the maximum number of iterations, increase the current number of iterations by 1 and repeat step B3.

[0067] B6. Output the optimal solution and obtain the optimal kernel parameter g and the optimal penalty factor C.

[0068] In the method of the present invention, the optimal kernel parameter g and the optimal penalty factor C are obtained, and these parameters can be used to configure the SVM model to predict the corrosion rate. The specific steps include:

[0069] Model configuration: Apply the optimal kernel parameter g and the optimal penalty factor C to the initial configuration of the SVM.

[0070] Data preparation: Prepare a training dataset with representative and relevant factors of the internal corrosion behavior as input.

[0071] Model training: Use the prepared training set and configured parameters to train the SVM.

[0072] Validate the model: Use the test set to verify the performance and predictive ability of the model to ensure that the model can accurately predict the corrosion rate.

[0073] Application prediction: Use the trained model to predict corrosion rate for new or unknown data. Input features into the model to get the predicted value of corrosion rate.

[0074] The step of evaluating the prediction results is also included: S5. Evaluating the prediction results according to relevant evaluation indicators; wherein the relevant evaluation indicators specifically include: mean absolute error MAPE, root mean square error RMSE, determination coefficient R 2 .

[0075] Furthermore, the calculation formula of the mean absolute error MAPE is:

[0076] The calculation formula of root mean square error RMSE is:

[0077] Coefficient of determination R 2 The calculation formula is:

[0078] In the above formula, n is the number of samples, y is the actual value, is the predicted value, is the average of the actual numbers.

[0079] Among the above three evaluation methods, the smaller the mean absolute error (MAPE) and the root mean square error (RMSE), the more accurate the prediction results are. 2 The closer the value is to 1, the more accurate the prediction result is.

[0080] In order to prove that the IWOA-SVM established by the method of the present invention has certain advantages over other methods, the PSO-SVM and WOA-SVM oil and gas pipeline corrosion rate prediction models are established at the same time to compare the prediction effects of various methods. The specific results are as follows: Figure 2 As shown in the figure, the overall prediction results of the IWOA-SVM model are closer to the true value, and the model has strong stability. The mean absolute error (MAPE) and root mean square error (RMSE) of the PSO-SVM, WOA-SVM and IWOA-SVM oil and gas pipeline internal corrosion rate prediction models are shown in Table 1. It can be seen from the table that the R2 of IWOA-SVM is 0.9806, which is the closest to 1 among all models, while the root mean square error (RMSE) is 0.0450 and the mean absolute error (MAPE) is 1.6202, which is the smallest among all models. It can be seen that the IWOA-SVM model has better prediction accuracy and generalization ability than other models, and can provide relevant staff with a more reliable reference for internal corrosion rate.

[0081] Table 1 Comparison of model prediction performance evaluation indicators

[0082]

[0083] The present invention improves the traditional whale method and combines it with the SVM method to propose the IWOA-SVM method. The improvements include introducing adaptive weights and nonlinear convergence factors, balancing global search and local development capabilities, so that it has both strong global search capabilities and is not easy to fall into local optimal solutions. The present invention combines the improved WOA model with the SVM method to achieve high-precision prediction of corrosion in in-service oil and gas pipelines and ensure the safety of in-service oil and gas pipeline operations.

[0084] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. A method for predicting corrosion rate in oil and gas pipelines based on IWOA-SVM, characterized in that: The following steps are involved: S1. Select factors that are representative and relevant to the internal corrosion behavior during the operation of oil and gas pipelines as input variables; S2. Preprocess the input variables and organize the processed data into data sets; S3. Divide the data in the dataset into a training set and a test set; S4. Establish an oil and gas pipeline corrosion rate prediction model based on IWOA-SVM and predict the internal corrosion rate; The establishment of the oil and gas pipeline corrosion rate prediction model based on IWOA-SVM in step S4 specifically includes the following sub-steps: S41. Use SVM as the basic model for corrosion rate in oil and gas pipelines; S42. Improve the IWOA method; S43. Use the improved IWOA method to optimize the basic model; In the step S42, the IWOA method is improved, and the calculation method of the convergence factor a, the local search update method X(t+1) and the weight ω(t) in the IWOA method are improved. The specific improvements are as follows: The calculation formula of the optimized convergence factor a is: In the formula, a ini with a fin is the initial and final value of the convergence factor, t is the current iteration number, T max is the maximum number of iterations; The linearly changing inertia weight is changed into a nonlinearly changing adaptive weight. The calculation formula of the local search update X(t+1) after the change is: Where ω(t) is the adaptive weight that changes with the number of iterations t, is the rate at which the inertia weight changes dynamically with the number of iterations, is the current optimal individual position, X(t) is the current individual position, A is the coefficient vector, D is the distance between the current individual position and the optimal individual position, b is the spiral shape constant, l is a random number between [-1,1], and p is a random number between [0,1]; The calculation formula of the adaptive weight ω(t) is: In the formula, ω max ,ω min are the maximum and minimum values ​​of the inertia weight respectively.

2. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 1 is characterized in that: The factors that are representative and relevant to the internal corrosion behavior in step S1 specifically include: CO2 partial pressure, CO2 concentration, temperature, pH value, medium flow rate, Cl - concentration.

3. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 1 is characterized in that: The specific steps of preprocessing the input variables in step S2 are: normalizing the data, wherein the calculation formula for data normalization is: Where X is the input variable vector, X min is the minimum value of the input variable vector, X max is the maximum value of the input variable vector, and X' is the normalized input variable vector.

4. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 1, characterized in that: The step S41 specifically includes the following sub-steps: S411. Set the total sample size and determine the input-output relationship model; S412. Establish constraints to optimize the input-output relationship model; S413. Introduce the kernel function and perform classification mapping on the samples.

5. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 1, characterized in that: The specific implementation steps of step S43 include: B1. Initialize the parameter weights and thresholds of SVM and initialize IWOA; B2. Set the population size N and the maximum number of iterations T max , iteration number t = 0, the kernel parameter g of SVM and the penalty factor C are used as the position vector of IWOA; B3. Update the nonlinear convergence factor and adaptive weight, calculate the coefficient vector A, and initialize the random number; B4. Update individual location information according to the A value; B5. Determine whether the number of iterations reaches the maximum number of iterations; B6. Output the optimal solution and obtain the optimal kernel parameter g and the optimal penalty factor C.

6. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 5, characterized in that: The step B5 specifically includes the following sub-steps: when the iteration number reaches the maximum iteration number, execute step B6; when the iteration number does not reach the maximum iteration number, increase the current iteration number by 1 and repeat step B3.

7. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 1, characterized in that: The step of evaluating the prediction results is also included: S5. Evaluating the prediction results according to relevant evaluation indicators; wherein the relevant evaluation indicators specifically include: mean absolute error MAPE, root mean square error RMSE, determination coefficient R 2 .

8. The method for predicting corrosion rate in oil and gas pipes based on IWOA-SVM according to claim 7, characterized in that: The calculation formula of the mean absolute error MAPE is: The calculation formula of root mean square error RMSE is: Coefficient of determination R 2 The calculation formula is: In the above formula, n is the number of samples, y is the actual value, is the predicted value, is the average of the actual numbers.

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