Method for predicting service life of furnace tube of converter based on machine learning

Abstract

The invention relates to the field of material performance evaluation and life prediction, and discloses a converter furnace tube life prediction method based on machine learning, which is suitable for creep life prediction of a high-temperature furnace tube in a complex temperature environment and can be applied to industries such as machine manufacturing, petrochemical engineering and energy equipment. The method provides technical support for safety and replacement decision of chemical production, and comprises the following steps: collecting and processing furnace tube material data, and establishing a creep database; mining an analytic formula of the life and the key factors in combination with a symbol regression algorithm and physical law constraints; through data set and physical verification, the formula is ensured to be accurate and reliable; and in combination with finite element analysis software, visualizing a life prediction result. According to the method, the service life prediction system suitable for the high-temperature furnace tube in the complex temperature environment is constructed through the four-stage technical process of database establishment, symbolic regression modeling, model verification and service life visualization, and the method has engineering application value.

Description

Technical Field

[0001] This invention relates to the field of material performance evaluation and life prediction, specifically to a method for predicting the life of converter tubes based on machine learning. Background Technology

[0002] Steam reformers are crucial production units in petrochemical enterprises, and the reformer tubes are their key components. During production, the reformer utilizes natural gas and steam to react within the tubes, generating hydrogen, carbon monoxide, and carbon dioxide, providing feedstock for downstream production units. The operating temperature of the reformer tubes is typically 700-950℃, and the materials used are HP40 or HK40 (both high-temperature resistant Fe-Cr-Ni based austenitic alloys, differing in Cr, Ni, and trace elements). The designed lifespan is 100,000 hours. However, due to overheating or accidental damage, reformer tube failure can occur before the designed lifespan, often leading to unexpected plant shutdowns and significant losses. Therefore, assessing the damage condition and remaining lifespan of the tubes is critical. The furnace chamber of a large top-fired reformer is a very large... The box-shaped structure has the burner located at the top of the furnace, with the flue gas descending. However, the flue gas flow inside the furnace is very complex, including both flue gas flow and heat transfer along the circumference and height of the furnace tubes. The temperature distribution on the outer wall of the top-fired converter tubes is closely related to the spatial distribution of the flue gas temperature in the radiant chamber. The uneven flue gas velocity in the radiant furnace causes uneven heating of some furnace tubes, resulting in local overheating. The lifespan of the furnace tubes depends on the point of highest temperature. Currently, predicting the creep life of furnace tubes with such uneven temperature distribution remains a major challenge.

[0003] Traditional metallographic testing methods for conversion furnace tubes can only provide operational precautions and temperature limits during furnace operation through microscopic observation, but cannot directly provide the corresponding lifespan of the furnace tubes. Furthermore, these methods are time-consuming and labor-intensive, and the high cost of furnace tubes leads to significant economic losses from shutdowns for maintenance during production. They also fail to provide accurate predictions. Traditional methods focus on the relationship between temperature, stress, and creep life, while neglecting the relationship between process or program parameters and creep life. Commonly used life prediction methods, such as the classic reference model Larson-Miller and similar reference models Manson-Haferd, predict material fracture life by fitting experimental data. Although widely used, these methods have limitations, including discrepancies in prediction results due to variations in furnace tube material constants and failure to consider tertiary creep damage. They also cannot provide creep life results at temperatures outside of experimental conditions. Data-driven technologies (such as machine learning) can improve the accuracy of solutions to simple or complex problems. Some studies have used machine learning algorithms to predict the creep life of steel alloys; however, modern data-driven technologies and traditional methods often cover newly manufactured materials and do not fully consider the impact of the process history of in-service components on creep behavior and remaining lifespan.

[0004] This invention presents a machine learning-based method for predicting the lifespan of converter tubes. This method addresses the impact of uneven temperature distribution and service history on creep lifespan, and visualizes the lifespan distribution of high-temperature tubes. By predicting tube lifespan, potential failure risks or safety hazards caused by uneven temperature distribution and aging can be identified in advance, ensuring equipment and personnel safety. Visualized lifespan distribution enables targeted preventative maintenance, reducing unplanned downtime and avoiding cost waste from premature replacement or exceeding service life due to misjudgment. It also allows for rational planning of spare parts procurement and replacement cycles, optimizing resource allocation, reducing overall maintenance expenses, and enabling more confident production planning. Furthermore, it reduces conservative operations such as reduced load due to concerns about equipment failure, ensuring the converter operates stably and efficiently over the long term. Therefore, this invention proposes a machine learning-based method for predicting the lifespan of converter tubes to overcome the shortcomings of existing technologies. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a machine learning-based method for predicting the lifespan of converter tubes. This method solves the problem of uneven lifespan distribution caused by uneven temperature distribution in converter tubes. It also considers the material's service history to obtain the creep lifespan of the tubes, making the converter tube lifespan prediction method more economical and safer in the petrochemical field.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the lifespan of converter tubes based on machine learning, comprising: S1. Collect and process creep data of converter tube materials, and create a creep database of converter tube materials through data preprocessing and feature filtering; S2. Process the creep database, introduce a symbolic regression algorithm, and set operators and constraints in combination with the physical laws of material creep to automatically mine analytical expressions of life and key factors. S3. Verify and validate the accuracy and reliability of the analytical expressions for the lifespan and key factors through multi-dataset verification and physical rationality verification. S4. Using a finite element model of the converter tube, calculate the temperature field and stress field data of the converter tube, and combine the verified and validated analytical expression of the life and key factors with the temperature field and stress field data to output a visualized life prediction result.

[0007] Preferably, in step S1, the creep data includes the metallic composition, mechanical properties, and high-temperature structural properties of the Fe-Cr-Ni based austenitic heat-resistant alloy of the converter tube; The operation of processing creep data of converter tube materials includes: expanding the creep data using Bayesian bootstrapping, and resampling multiple regenerated datasets based on weights. Bayesian bootstrapping is suitable for scenarios with small sample data, and specifically includes the following steps: (1) Constructing the empirical distribution function: Let For observational samples from an unknown population, the samples are first... Arranged in ascending order, we obtain the ordinal statistics. Construct the empirical cumulative distribution function for: ; (2) Generate Dirichlet distribution weights: Generate weights on the interval (0,1) 1 independent and identically distributed random number Sort them in ascending order, and then calculate the weights. : ; in: , ; (3) Generate regenerated samples: Use weights to perform weighted sampling on the original samples to generate regenerated samples. : ; in: , ; (4) Repeat the above steps: Repeat steps S1 to S3 Second-rate( To expand the data by multiple factors, multiple regenerated sample sets are obtained. These multiple regenerated sample sets are then merged to form the expanded data. After data expansion, the expanded dataset is used to measure the linear correlation between each input feature and the output feature (lifetime) by calculating the Pearson correlation coefficient. Features with a correlation coefficient value greater than or equal to 0.6 with lifetime are selected and used as input parameters for subsequent symbolic regression algorithms.

[0008] Preferably, the creep data of the processed converter tube material further includes: The input parameters are normalized using the Min-Max normalization method to map the features to the [0,1] interval; Logarithmically transform the furnace tube life, which is used as an output parameter, and perform normal distribution detection on the processed creep data; Finally, the creep data after the above processing is subjected to normal distribution detection to confirm whether the dataset meets the requirements of subsequent model processing.

[0009] Preferably, processing the creep database includes: dividing the creep database into a training set and a test set, with the training set being 70% and the test set being 30%. The symbolic regression algorithm is executed using the training set. By modifying parameters such as population size and generation number in the algorithm, iterative optimization is performed to discover analytical expressions for the lifespan and key factors that meet preset conditions.

[0010] Preferably, in step S2, the operator set includes: Unary operators “exp”, “log”, “sqrt”, “inv(x)=1 / x”; And binary operators "+", "*", "-", " / ", and "^".

[0011] Preferably, the operators and constraints include: Monotonicity constraint: used to ensure the rationality of the extracted analytical expression in terms of physical laws, that is, when the temperature or stress of the converter tube increases, the predicted life of the converter tube decreases monotonically. Dimensional consistency constraint: used to force the dimensions of each item in the analytical expression to be consistent, ensuring that the analytical expression is physically valid; Complexity constraint: By limiting the maximum number of nodes in the parsed expression, overfitting of the model is avoided and the simplicity of the expression is ensured.

[0012] Preferably, in step S3, the accuracy and reliability of the analytical expression for lifespan and key factors are verified and validated by calculating the coefficient of determination using a test set. and mean absolute error ; The coefficient of determination The mean absolute error is greater than or equal to 0.95. Less than or equal to 5%; The analytical expression for lifetime and key factors was applied to different batches of material data to verify the generalization error, which was less than or equal to 5%; mean square error. and mean absolute error The following formula is used for evaluation: Coefficient of determination : ; Mean square error : ; Mean Absolute Error : ; in, Represents the total number of data samples; The true value of the sample; These are the model's predicted values; The average of the true values ​​in the sample; Simultaneously, the analytical expression for the lifespan and key factors is applied to material data from different production batches or data under similar operating conditions to verify the generalization error, requiring a generalization error... Less than or equal to 5%.

[0013] Preferably, step S3 further includes: Physical law verification: The analytical expressions for the lifespan and key factors are verified by physical laws to ensure that the prediction results meet the following: lifespan decreases with increasing temperature; lifespan decreases with increasing stress (and conforms to the power law model); and the trend of lifespan change conforms to known materials science laws when the content of specific chemical elements (such as Cr, Ni, etc.) changes.

[0014] Dimensional consistency verification: Verify the dimensional consistency of the analytical expression again to ensure that the dimensions of the lifespan are consistent with those of the analytical expressions of the key factors.

[0015] Comparative verification: The analytical expressions for lifespan and key factors are compared with the prediction performance of at least one traditional machine learning model (such as support vector machine, random forest, etc.) under the same dataset partitioning and feature selection to verify the prediction accuracy.

[0016] Input the feature variables of the test set into the analytical expression and plot a scatter plot of the actual lifetime versus the predicted lifetime. It is required that more than 90% of the sample points fall within the range of ±5% of the actual value.

[0017] Preferably, step S4 further includes: Based on the temperature measurement data of the converter tube under actual operating conditions, a temperature distribution function of the converter tube is fitted. Based on the geometric parameters (such as outer diameter, wall thickness, length, etc.) and material physical properties (such as thermal conductivity, elastic modulus, etc.) of the converter tube, a finite element model of the converter tube is established in a finite element analysis software. In the finite element analysis software, the temperature field and stress field data of the converter tube under steady-state conditions are calculated based on the fitted temperature distribution function and other boundary conditions.

[0018] Preferably, in step S4, the analytical expressions for the lifespan and key factors after verification and validation are combined with the temperature distribution cloud map: The temperature and stress field data of each node extracted from the finite element model are used as input parameters and substituted into the analytical expression of the life and key factors after verification and validation to calculate the life value of the furnace tube corresponding to each node position. The calculated lifetime value is rewritten back into the finite element model of the converter tube in the form of a data field, thereby obtaining a lifetime distribution cloud map of the converter tube and realizing the visualization of the prediction results.

[0019] This invention provides a machine learning-based method for predicting the lifespan of converter tubes. It offers the following advantages: 1. The symbolic regression algorithm used in this invention can automatically mine the complex nonlinear relationship between multi-dimensional key factors such as material composition, temperature distribution, and stress field and creep life based on data, and more comprehensively capture the intrinsic mechanism of creep damage, reduce the prediction error introduced by artificial simplification of the model, and thus obtain higher prediction accuracy.

[0020] 2. This invention directly outputs a clear mathematical analytical expression through symbolic regression, intuitively revealing the quantitative correlation between furnace tube life and various key parameters. This enables engineers to clearly understand the influence weight of each factor, providing clear guidance for engineering decisions such as optimizing operating conditions and improving material composition. At the same time, it is also easy to embed into existing industrial design or equipment operation and maintenance systems.

[0021] 3. The symbolic regression algorithm of this invention does not require a pre-defined model structure and can integrate multi-dimensional dynamic data features for modeling. Therefore, it can flexibly adapt to the life prediction needs of different furnace types, material grades and specific operating conditions, making it more applicable to a wider range of scenarios than traditional methods.

[0022] 4. This invention can automatically mine and optimize formulas based on existing databases through symbolic regression, which greatly shortens the development cycle from data to practical models. At the same time, by introducing physical law constraints into the algorithm and performing subsequent verification, it ensures that the generated formulas have both data accuracy and physical reliability, thereby reducing the reliance on expensive and time-consuming experimental verification in the later stage and accelerating the application of prediction technology in industrial scenarios. Attached Figure Description

[0023] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a flowchart of the method for creating a creep database according to the present invention; Figure 3 This is a flowchart of the symbolic regression mining parsing expression method of the present invention; Figure 4 This is a flowchart of the parsing expression verification method of the present invention; Figure 5 This is a flowchart of the finite element method combined with visualization for lifetime prediction according to the present invention. Detailed Implementation

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] See attached document Figure 1 The present invention provides a method for predicting the lifespan of converter tubes based on machine learning, which may specifically include the following steps: Step S1: Create a creep database, collect and process creep data of furnace tube materials (e.g., Fe-Cr-Ni austenitic heat-resistant alloy). First, the raw data, including information such as the metal composition, mechanical properties, high-temperature structural properties and service history of Fe-Cr-Ni austenitic heat-resistant alloy, is expanded using the Bayesian bootstrapping method to be suitable for small sample data scenarios.

[0026] In one specific implementation, Bayesian bootstrapping includes: (1) Constructing the empirical cumulative distribution function : ; (2) Generate Dirichlet distribution weights: Generate weights on the interval (0,1) 1 independent and identically distributed random number Sort them in ascending order, and then calculate the weights. : ; in: , ; (3) Generate regenerated samples: Use weights to perform weighted sampling on the original samples to generate regenerated samples. ,in: , ; After data augmentation, features with a correlation of 0.6 or greater with lifetime were selected by calculating the Pearson correlation coefficient. The selected input parameters were then processed using the Min-Max normalization method, and the output parameters (lifetime) were logarithmically transformed to form a creep database for subsequent steps.

[0027] Step S2: Mining analytical expressions and processing the generated creep database. A symbolic regression algorithm is introduced to automatically mine analytical expressions related to lifespan and key factors. The creep database is divided into a 70% training set and a 30% test set. The symbolic regression algorithm is executed using the training set. Unary operators ("exp", "log", "sqrt", "inv(x)=1 / x") and binary operators ("+", "*", "-", " / ", "^") are set based on the physical laws of material creep. Monotonicity constraints, dimensionality consistency constraints, and complexity constraints are applied. Through iterative optimization, the algorithm obtains the results that meet the preset conditions (e.g., the coefficient of determination on the training set). An analytical expression that is greater than or equal to 0.95 and conforms to the laws of physics.

[0028] Step S3: Verify the analytical expression. Through multi-dataset verification and physical plausibility checks, verify the accuracy and reliability of the mined analytical expression. Calculate the coefficient of determination of the analytical expression using the partitioned test set. and mean absolute error and demand Greater than or equal to 0.95 Less than or equal to 5%.

[0029] In one specific implementation, the coefficient of determination Mean square error and mean absolute error The following formula is used for evaluation: ; ; ; in, Represents the total number of data samples; The true value of the sample; These are the model's predicted values; The average of the true values ​​in the sample; Step S3 also includes verification of physical laws, verification of dimensional consistency, and comparison with traditional machine learning models.

[0030] Step S4: Perform visualization prediction. Using a finite element model of the converter tube, calculate the temperature field and stress field data of the converter tube. Then, combine the verified and validated analytical expression with the temperature field and stress field data to calculate the lifetime value at each location on the tube and write it back into the finite element model. Finally, output a visualization of the lifetime prediction result, such as a lifetime distribution cloud map.

[0031] See attached document Figure 2In this embodiment, the goal of data acquisition and integration is to create a structured initial database for machine learning. First, the data acquisition object is defined as the commonly used material of the conversion furnace tube, specifically Fe-Cr-Ni based austenitic heat-resistant alloy. The acquired data information is multi-dimensional, with the aim of comprehensively characterizing various factors affecting the high-temperature creep performance of Fe-Cr-Ni based austenitic heat-resistant alloy.

[0032] Specifically, the collected data includes: Metal composition information: Record the mass percentage of each chemical element that constitutes the Fe-Cr-Ni based austenitic heat-resistant alloy, including at least the main alloying elements such as iron (Fe), chromium (Cr), and nickel (Ni), as well as elements that have a significant impact on high-temperature performance such as carbon (C), silicon (Si), manganese (Mn), molybdenum (Mo), and niobium (Nb). Each data record corresponds to a specific chemical composition analysis result.

[0033] High-temperature structural performance information: Records the performance data of Fe-Cr-Ni based austenitic heat-resistant alloys in high-temperature environments. This is the core part of the database. It mainly includes a series of creep test results conducted at different temperatures and stress levels. The key data points are the test temperature, the applied constant stress, and the time required for the material to fracture, i.e., creep life.

[0034] Service history information: Records the manufacturing and processing information of materials, including the production batch number of the material, the heat treatment process used (e.g., the temperature and time of solution treatment), etc. This information is used to trace performance fluctuations caused by differences in manufacturing processes.

[0035] After completing the detailed collection of the above-mentioned information, the data is structured and integrated. Each set of independent creep test data (including its corresponding metal composition, mechanical properties and service history information) is treated as an independent record, and creep life is used as the target output feature, while other information is used as input features. Finally, it is compiled into an initial database with a unified format, providing a data foundation for subsequent data expansion and feature selection steps.

[0036] See attached document Figure 2 This invention addresses the challenges of obtaining high-temperature alloy creep test data and the typically small sample size of the original database. It introduces a Bayesian bootstrapping method to expand the creep data and constructs multiple regenerated datasets by incorporating probability distributions. Compared to simple random sampling, the generated regenerated datasets more closely resemble the empirical distribution of the original data, effectively alleviating the problem of insufficient model training data in scenarios with small sample data.

[0037] The specific data augmentation process includes the following four steps: (1) Constructing the empirical distribution function: Let For observational samples from an unknown population, the samples are first... Arranged in ascending order, we obtain the ordinal statistics. Construct the empirical cumulative distribution function for: ; (2) Generate Dirichlet distribution weights: Generate weights on the interval (0,1) 1 independent and identically distributed random number Sort them in ascending order, and then calculate the weights. : ; in: , ; (3) Generate regenerated samples: Use weights to perform weighted sampling on the original samples to generate regenerated samples. ,in: , ; (4) Repeat the above steps: Repeat steps S1 to S3 Second-rate( To expand the dataset by a factor of 1, multiple regenerated sample sets are obtained. Finally, these multiple regenerated sample sets are merged to form an expanded dataset. The expanded dataset significantly increases the number of samples while maintaining the original data distribution characteristics, providing sufficient data support for the subsequent training of the symbolic regression model.

[0038] See attached document Figure 2 After data expansion, this invention establishes a high-temperature metal database using the expanded dataset and optimizes the input features through a feature selection process. The goal is to identify and remove redundant variables with low correlation to furnace tube life prediction, thereby reducing the complexity of the subsequent symbolic regression algorithm in searching for the optimal analytical expression and improving the convergence speed and physical focus of the model. In this embodiment, the Pearson correlation coefficient is used as an indicator to measure the degree of linear correlation between the input features and the output features (life). After calculating the Pearson correlation coefficient between each input feature and life, this invention sets a clear selection criterion: only features with a correlation coefficient greater than or equal to 0.6 with creep life are retained. For example, in alloy composition, some minor material components with weak or insignificant effects on creep life may be removed because their correlation coefficient is lower than this threshold.

[0039] Meanwhile, models such as random forests were used to summarize and assist in the selection of feature distributions in the feature dataset. This further confirmed that the selected feature set had high information content and low redundancy. Through the above correlation analysis and model assistance, a concise feature subset with high correlation to lifespan was finally generated as the input parameters for the subsequent symbolic regression algorithm, forming an expanded dataset. The feature selection process ensured that the model focused only on the key physical quantities most relevant to creep lifespan.

[0040] See attached document Figure 2 In order to eliminate the influence of different physical dimensions and numerical ranges on model training and optimize data distribution, this invention performs data preprocessing techniques on the expanded dataset, including normalization transformation of input parameters and logarithmic transformation of output parameters, while cleaning the data to ensure that the dataset fully meets the input requirements of subsequent machine learning models.

[0041] Specifically, for the input parameters, a Min-Max normalization method is used to process them. The value of each selected feature descriptor is linearly mapped to the closed interval [0,1]. This avoids the problem that individual features (such as temperature and stress) may dominate the model training due to their numerical range being much larger than that of other features (such as chemical composition percentage).

[0042] For the creep life as an output parameter, a logarithmic transformation is performed. Since the creep life values ​​of materials often span multiple orders of magnitude, the data distribution exhibits a significant skewness. By taking the logarithm of the life data, the numerical range can be effectively compressed and the data distribution adjusted to be closer to a normal distribution. This processing helps to improve the stability and convergence efficiency of the subsequent symbolic regression model when searching the solution space.

[0043] While performing normalization and logarithmic transformation, the data also includes data cleaning, specifically handling missing and outlier values. After completing all the above optimization processes, the processed data is stored to form the final database that can be directly used for model training and validation.

[0044] See attached document Figure 3 In order to build machine learning models, train parameters, and perform subsequent independent performance verification, this invention requires partitioning the final output database file. The partitioning operation divides the original dataset into two non-overlapping subsets, namely the training set and the test set.

[0045] Specifically, this embodiment divides the dataset in the following proportions: 70% of the creep database is divided into a training set for model training, parameter iteration, and optimization of the formula structure of the symbolic regression algorithm; the remaining 30% of the data is divided into a test set. The test set is independent of the training process and is used to objectively evaluate the accuracy and verify the reliability of the trained analytical expressions, so as to ensure that the model has good generalization ability and prediction performance.

[0046] The partitioning process uses random sampling to ensure that the training and test sets maintain consistency in data distribution, thereby avoiding evaluation bias caused by differences in data distribution. After partitioning, the two datasets will serve as the input for the subsequent symbolic regression model and the basis for model validation.

[0047] See attached document Figure 3 In order to ensure that the symbolic regression algorithm can extract analytical expressions with clear physical meaning, this invention predefines a series of basic operators. The selection of these operators is based on the physical mechanism of material creep failure, providing the algorithm with a mathematical basis for constructing formula structures that conform to physical laws. In specific implementations, these operators can be provided to the symbolic regression algorithm through custom functions (e.g., encapsulated by make_function in the Python environment).

[0048] Specifically, the operator set includes unary and binary operators. Unary operators include: the exponential function exp, used to simulate the exponential decrease in creep life with increasing temperature; the logarithmic function log, used to describe the logarithmic cumulative effect of damage; the square root function sqrt, used to reflect certain time-related cumulative damage mechanisms; and the reciprocal function inv(x)=1 / x, used to adapt to the inverse relationship between stress and creep life. Binary operators include addition "+", multiplication "*", subtraction "-", division " / ", and the power function "^". These binary operators are used to reflect the coupling effect between multiple factors such as temperature, stress, and material composition. For example, power functions can be used to construct the square term of temperature or the power term of stress to describe the nonlinear damage process.

[0049] To further guide the search direction of symbolic regression and avoid generating expressions that are mathematically valid but violate physical laws, this invention also sets the following physical constraints: Monotonicity constraint: Ensures the rationality of the extracted analytical expression in terms of physical laws. Specifically, constraints are applied by means of custom loss functions, so that when the value of the variable representing temperature or stress increases in the expression, the predicted lifetime value decreases monotonically. The monotonicity constraint directly corresponds to the basic law of creep failure of materials at high temperatures.

[0050] Dimensional consistency constraint: This constraint requires that all components involved in the calculation in the final generated analytical expression must be consistent in terms of units. For example, if the unit of lifespan is hours, then the calculation result of all terms in the expression must be in the unit of time. Dimensional consistency constraint eliminates meaningless formulas with mismatched units and ensures the physical validity of the expression.

[0051] Complexity constraints: By limiting the maximum number of nodes in the parsed expression (e.g., setting it to 20 to 30 nodes), the complexity of the formula can be controlled. This can effectively avoid the problem of decreased generalization ability caused by overfitting the training data, and also ensure that the final expression has a concise structure that is easy for engineers to understand and apply.

[0052] See attached document Figure 3 After completing the design of operators and physical constraints, this invention uses a partitioned training set to train a symbolic regression model to uncover potential lifetime prediction formulas. The training process of the symbolic regression model is based on an iterative evolution algorithm, specifically implemented as follows: First, by modifying the population size and generation number parameters in the symbolic regression training model, a population consisting of 100 to 200 initial expressions is randomly generated in the initial stage. These initial expressions are formed by randomly combining operators and input features.

[0053] Subsequently, the symbolic regression training model was modified to enter the iterative evolution phase. In each iteration, the fitness of each expression in the population was first evaluated. The fitness was calculated based on the expression's predictive performance on the training set, and its specific fitness function was determined by... for: ; in, The root mean square error, fitness value The fitness is inversely proportional to the prediction error of the expression; that is, the smaller the error, the higher the fitness.

[0054] After completing the fitness assessment, a selection mechanism is used to retain the top 30% of expressions in the population based on fitness, while eliminating the remaining expressions. Then, crossover and mutation operations are performed on the retained high-fitness expressions to generate new expressions, thus forming the next generation of the population. The iterative process continues until the preset number of generations is reached.

[0055] After the iteration process is completed, the optimal formula is selected based on its coefficient of determination on the training set. The expression must be greater than or equal to 0.95 and fully conform to all the physical laws set. Finally, the selected expressions are used to generate corresponding visual expression trees through visualization tools. The operators and terms in the expression trees are then merged and simplified to obtain the simplified lifetime prediction formula for subsequent verification and application.

[0056] See attached document Figure 4 This invention first uses a segmented test set that was not used in model training to objectively evaluate the prediction accuracy of the lifetime prediction formula. This objective evaluation is accomplished by calculating a series of pre-defined statistical indicators. Specifically, the input feature data from the test set is substituted into the lifetime prediction formula to obtain a set of predicted lifetime values. These predicted lifetime values ​​are then compared with the corresponding actual lifetime values ​​in the test set, and their coefficient of determination is calculated. With mean absolute error .

[0057] In this embodiment, the accuracy qualification standard is set as: determination coefficient. The value is greater than or equal to 0.95, and the mean absolute error is... The value is less than or equal to 5%.

[0058] This invention will also be applied to other datasets for validation. These datasets may come from different production batches of materials or from other converters with similar operating conditions. The generalization error will be assessed on these new datasets, and the mean absolute error will be required. It remains less than or equal to 5%, used to confirm that it is not limited to the original training data and has the reliability to be promoted and applied in actual engineering.

[0059] See attached document Figure 4 First, to intuitively evaluate the fitting effect of the lifespan prediction formula, this invention performs a visualization verification. Specifically, all feature variables in the test set are used as inputs and substituted into the determined symbolic regression formula to calculate the predicted lifespan value corresponding to each sample point. Subsequently, a scatter plot is drawn with the actual lifespan as the x-axis and the predicted lifespan as the y-axis. On the scatter plot, more than 90% of the sample data points are required to fall within the range of ±5% of the actual value. The range is represented in the plot as a band-shaped area formed by two straight lines centered on the y=x line and bounded by y=1.05x and y=0.95x.

[0060] After completing the verification of quantitative indicators and fitting effects, this invention verifies the conformity of the symbolic regression formula that meets the accuracy requirements with physical laws. This is to eliminate any possible mathematical structures that only fit mathematically but violate physical mechanisms. The verification process includes: Monotonicity verification: The monotonicity of core variables (e.g., temperature T, stress σ) is determined. The specific method is to change only the value of the variable to be measured for all other variables except the variable to be measured, and calculate its corresponding lifetime prediction value. For example, when verifying the effect of temperature T, the value of T is set to 800℃, 900℃, and 1000℃ respectively and substituted into the formula to verify whether the predicted lifetime shortens with increasing temperature. Similarly, it is verified whether the predicted lifetime decreases when the stress increases, and whether the predicted lifetime increases when the content of certain specific chemical elements increases. Verifying the predicted lifetime requires that the monotonicity of all core variables conforms to known physical laws.

[0061] Empirical Formula Comparison and Verification: The lifetime prediction obtained by this invention is compared and verified with that in the field of materials science. Under the same input conditions, the predicted lifetime is calculated using the symbolic regression formula and the classical reference model Larson-Miller formula, respectively, and the calculation results of the two are compared. The error requirement for the comparison and verification is within ±15%.

[0062] Creep mechanism conformity verification: Review the mathematical structure of the formula, eliminate mathematical forms that obviously violate the three-stage characteristics of material creep (i.e., initial creep stage, steady-state creep stage, and accelerated creep stage), and ensure that the overall structure of the formula is consistent with the physical process of creep damage accumulation.

[0063] See attached document Figure 4 This invention first performs a final dimensional consistency check on the life prediction formula that has passed all verification steps. The check aims to ensure the absolute correctness of the formula in the physical dimension. Specifically, each variable in the formula (such as temperature, stress, chemical element content) is assigned its corresponding SI base unit or derived unit, and the dimension of the calculation result is derived item by item according to the mathematical operators in the formula (such as addition, subtraction, multiplication, division, exponentiation, logarithm, exponentiation). The process requires that all terms added or subtracted in the formula must have the same dimension, and the parameters of special functions such as exponential functions and logarithmic functions must be dimensionless. Finally, the check needs to confirm that the final dimension of the result calculated by the entire expression is completely consistent with the dimension of life (e.g., hours). Any formula that is inconsistent in dimension will be excluded.

[0064] To further confirm the performance of the technical solution adopted in this invention, this invention also performs model comparison verification. The model comparison verification compares the performance of the life prediction formula obtained by this invention through symbolic regression with several other machine learning models under the same conditions. The models used for comparison include: random forest (RF), decision tree (DT), support vector machine (SVM) and artificial neural network (ANN).

[0065] The specific implementation method of this comparative verification is as follows: Use identical, partitioned training and test sets; Random forest, decision tree, support vector machine and artificial neural network models were trained on the training set respectively, and hyperparameters were optimized by methods such as grid search to ensure that each model was in its optimal performance state. After training is completed, the performance of the four models and the symbolic regression formula obtained in this invention is evaluated using the test set. The performance metric used for evaluation is the coefficient of determination calculated on the test set. and mean absolute error ; Through this comparative verification, the symbolic regression formula of this invention is... Value and The value is compared with the corresponding values ​​of the other four models to quantitatively demonstrate the specific performance of the method provided by this invention in terms of prediction accuracy and generalization ability.

[0066] See attached document Figure 5 This invention first utilizes a finite element model of a converter furnace tube. The finite element model is established based on the furnace tube's geometric dimensions, material properties, thermal boundary conditions (such as internal fluid temperature and flow rate, external furnace temperature, radiative heat transfer coefficient, etc.) and service history. By performing thermo-mechanical coupling calculations on the finite element model, the temperature field data of the furnace tube under steady-state or quasi-steady-state conditions can be obtained. The temperature field data records in detail the instantaneous temperature values ​​at each grid node of the inner wall, outer wall, and inside the tube wall.

[0067] Since the subsequent analytical expression calculation requires continuous function input, this invention needs to transform the discrete temperature field data obtained from finite element calculation into a continuous temperature distribution function. The fitting process aims to establish the functional relationship between the temperature at any position in the furnace tube wall thickness direction and the coordinates of that position.

[0068] Specifically, the fitting process in this step includes: Data extraction: Extract discrete temperature data points along the wall thickness of the furnace tube from the finite element model calculation results, including the coordinates of each node (e.g., radial coordinates with the inner wall of the furnace tube as the origin and the direction towards the outer wall as the positive direction) and its corresponding temperature. Function selection and fitting: Based on the physical laws of heat transfer in furnace tubes, a suitable function form (e.g., polynomial function or exponential function) is selected as the fitting model. The selected function is fitted using the least squares method with the extracted discrete data points to finally obtain a continuous function characterizing the radial temperature distribution of the furnace tubes. Through function fitting, this invention transforms the discrete temperature data provided by the finite element model into a continuous function form that can be directly input into the analytical expression, thereby enabling the calculation of the temperature value of any micro-element or micro-structure point in the furnace tube wall thickness direction, providing accurate temperature input for subsequent life calculation.

[0069] See attached document Figure 5 After obtaining the temperature distribution function of the furnace tube, this invention requires the establishment of a two-dimensional axisymmetric finite element model to describe the physical behavior in order to further solve the stress response under the combined action of thermal and mechanical loads. The establishment and solution process of the two-dimensional axisymmetric finite element model aims to obtain the stress distribution function of the furnace tube along the wall thickness direction. The specific modeling and solution steps are as follows: Geometric model creation and mesh generation: First, a three-dimensional model is created based on the actual design dimensions of the converter tube. The three-dimensional model only needs to define the inner diameter, outer diameter, and length of the tube. Then, the geometric model is meshed, discretized into a set of finite elements. In this embodiment, four-node axisymmetric elements are used for mesh generation, and mesh refinement is performed in areas near the inner wall of the tube where stress gradients may be large, to ensure the convergence and accuracy of the calculation results.

[0070] Material property assignment: The 3D model is assigned physical properties that correspond to the actual furnace tube material (Fe-Cr-Ni based austenitic heat-resistant alloy). These physical properties are functions of temperature, meaning their values ​​change with temperature. Specifically, they include: elastic modulus, Poisson's ratio, thermal conductivity, coefficient of thermal expansion, and constitutive relations describing the material's creep behavior (e.g., creep parameters defined by Norton's creep law). These temperature-varying material property data are predefined and input into the finite element software's material library.

[0071] Load and boundary conditions applied: Thermal load: The fitted radial temperature distribution function of the furnace tube is applied as a thermal load to the entire finite element model. The temperature field is the fundamental cause of thermal stress in the furnace tube. Mechanical load: Based on the actual operating conditions of the converter, a uniformly distributed pressure is applied to the inner wall surface of the three-dimensional model. The pressure value is equal to the operating pressure of the process gas inside the furnace tube. Constraints: To prevent rigid body displacement of the 3D model during the solution process, necessary displacement constraints must be applied. For example, an axial displacement constraint can be applied to one end of the 3D model. Model Solving and Result Extraction: After completing all the above settings, start the finite element solver to perform a steady-state solution for the thermo-structural coupling problem. The solver will calculate the displacement and stress of each node in the three-dimensional model based on the input material properties, loads and boundary conditions. After the solution is completed, the equivalent stress distribution data of the furnace tube along the wall thickness direction is extracted. Similar to the processing of the temperature field, by fitting a function to these discrete stress data points, a continuous function characterizing the radial stress distribution of the furnace tube is finally obtained.

[0072] Thus far, through finite element simulation, two key physical quantity functions describing the state of the furnace tube under specific operating conditions have been obtained: the temperature distribution function and the stress distribution function. These two functions will serve as direct inputs for the next step of substituting analytical expressions into the point-by-point life calculation.

[0073] See attached document Figure 5 After obtaining the temperature distribution function and stress distribution function describing the state of the furnace tube, the core task of this invention is to use these continuous physical field data to drive the extracted lifetime prediction analytical expression, thereby calculating the creep lifetime of the furnace tube at each point along the wall thickness direction.

[0074] To achieve this goal, the present invention employs a secondary development script for data interaction and computation. This script (e.g., using Python combined with APDL command streams) is designed to automatically perform the following operations: Data interface establishment: The secondary development script first establishes a communication interface with the post-processing module of the finite element analysis software (such as ANSYS). Through the communication interface, the secondary development script can directly read and call the results of the solved finite element model. Physical field function integration: The secondary development script loads the fitted temperature distribution function and stress distribution function, and integrates the final determined lifetime prediction formula as a built-in function module into the script; Point-by-point iterative calculation: The core function of the secondary development script is to perform point-by-point iterative calculations along the radial path (i.e., the wall thickness direction) of the furnace tube. Specifically, this path is discretized into... There are equidistant integration points, among which The value is usually greater than 100 to ensure calculation accuracy; Lifetime distribution data generation: The script executes the above iterative process repeatedly until all data on the radial path has been traversed. After calculating the integral points, the script integrates the coordinates of all integral points and their corresponding life prediction values ​​to generate a discrete dataset that describes the life distribution of the furnace tube along the wall thickness direction. The discrete dataset accurately reveals the location of the weakest point and the shortest life of the furnace tube, which usually occurs in the area where the combined effects of temperature and stress are most severe. The life distribution data will serve as the basis for the final visualization.

[0075] See attached document Figure 5 This invention, after calculating the creep life point-by-point along the furnace tube wall thickness, presents the discrete life distribution data in an intuitive and clear graphical manner. The visualization process aims to transform abstract numerical results into graphics with engineering guidance significance, thereby identifying the bottleneck locations of the furnace tube's lifespan under specific operating conditions. Specific presentation methods include: Radial lifetime distribution curve plotting: Data mapping: The generated discrete dataset is processed to plot a two-dimensional curve between the radial position coordinates of the furnace tube (e.g., from the inner wall to the outer wall) and the corresponding predicted creep life; Key information annotation: On the two-dimensional curve, the lowest lifespan point in the direction of furnace tube wall thickness and its corresponding radial position are clearly marked. The radial position is determined as the overall creep lifespan of the furnace tube in that section. This information is crucial for maintenance personnel to formulate maintenance and replacement plans. Lifetime gradient display: The graph visually shows the gradient change of the furnace tube life along the wall thickness direction, revealing the trend of rapid change in the furnace tube life from the high temperature and high stress inner wall to the relatively low temperature and low stress outer wall.

[0076] Overlay of lifetime contour plots from finite element post-processing results: Data interpolation: The discrete lifetime prediction values ​​are mapped back to the individual mesh nodes of the two-dimensional axisymmetric finite element model through the post-processing function of the finite element software (e.g., through interpolation algorithms); Cloud map generation: Generate a life prediction cloud map on the cross-section of the furnace tube. In the life prediction cloud map, different color areas represent different predicted life values. Warm colors (such as red) are usually used to represent low life areas (high danger areas), and cool colors (such as blue) are used to represent high life areas (low danger areas). Engineering implications: The creep life prediction cloud map can be directly compared with the temperature field and stress field cloud maps calculated by finite element method, allowing engineers to intuitively see whether the minimum area of ​​creep life matches the known temperature and stress concentration areas (e.g., the inner wall, near the weld), thereby making a physical judgment on the prediction results; Through the above visualization, this invention not only outputs a lifespan prediction value, but also provides a global view of the lifespan distribution inside the furnace tube, improving the practicality, intuitiveness, and engineering guidance value of furnace tube lifespan assessment.

Claims

1. A machine learning based reformer tube life prediction method, characterized by, The method comprises the following steps: S1, collecting and processing the creep data of the converter tube material, creating a creep database of the converter tube material through data preprocessing and feature screening; S2, processing the creep database, introducing symbolic regression algorithm, and setting operators and constraint conditions combined with the physical law of material creep for automatically mining the analytical expression of life and key factors; S3, verifying and checking the accuracy and reliability of the analytical expression of life and key factors through multi-data set verification and physical rationality checking; S4, calculating the temperature field and stress field data of the converter tube through the finite element model of the converter tube, combining the analytical expression of life and key factors after verification and checking with the temperature field and stress field data, and outputting the visual life prediction result.

2. The machine learning based reformer tube life prediction method of claim 1, wherein, In the S1 step, the creep data includes the metal composition, mechanical properties, and high-temperature structural properties of the Fe-Cr-Ni-based austenitic heat-resistant alloy of the converter tube; The operation of processing the creep data of the converter tube material includes: using the Bayesian bootstrap method to expand the creep data; Using the creep data of the converter tube material, the features with a life correlation greater than or equal to 0.6 are selected by calculating the Pearson correlation coefficient, and the features with a life correlation greater than or equal to 0.6 are input parameters for processing the symbolic regression algorithm.

3. The machine learning based reformer tube life prediction method of claim 2, wherein, The processing of the creep data of the converter tube material also includes: Using the Min-Max normalization method to normalize the input parameters for mapping the features to the [0, 1] interval; Logarithmically transforming the converter tube life as an output parameter, and performing normal distribution detection on the processed creep data.

4. The machine learning based reformer tube life prediction method of claim 1, wherein, The processing of the creep database includes dividing the creep database into a training set and a test set; Using the training set to execute the symbolic regression algorithm, iterating by modifying the population size and evolution algebra, and outputting the analytical expression of life and key factors that meet the preset conditions.

5. The machine learning based reformer tube life prediction method of claim 1, wherein, In the S2 step, the operators include unary operators and binary operators: The unary operators include "exp", "log", "sqrt", and "inv(x)=1 / x"; The binary operators include "+", "*", "-", " / ", and "^".

6. The machine learning based reformer furnace tube life prediction method of claim 1, wherein, The operators and constraint conditions include: Monotonicity constraint for ensuring that the life decreases when the converter tube temperature rises or the stress increases; Dimension consistency constraint for forcing the analytical expression of life and key factors to have consistent dimensions; Complexity constraint for limiting the maximum node number of the analytical expression of life and key factors.

7. The machine learning based reformer tube life prediction method of claim 4, wherein, In the S3 step, the accuracy and reliability of the analytical expression of life and key factors are verified and checked by calculating the determination coefficient and the average absolute error through the test set; The determination coefficient is greater than or equal to 0.95, and the average absolute error is less than or equal to 5%. The life and key factor analytical expression is applied to material data of different batches to verify a generalization error, which is less than or equal to 5%.

8. The machine learning based reformer tube life prediction method of claim 1, wherein, The S3 step further comprises: Physical law verification is performed on the converter tube life and the life and key factor analytical expression; Dimension consistency verification is performed to ensure that the life and key factor analytical expression is dimensionally consistent; The life and key factor analytical expression is compared with a traditional machine learning model for verification.

9. The machine learning based reformer furnace tube life prediction method of claim 1, wherein, The S4 step further comprises: According to the geometric parameters and material physical performance parameters of the converter tube, a finite element model of the converter tube is established, and calculation of temperature field and stress field data of the converter tube is performed in a finite element analysis software.

10. The machine learning based reformer tube life prediction method of claim 9, wherein, In the S4 step, the verified and checked life and key factor analytical expression is combined with the temperature distribution cloud map: The temperature field and stress field data are input into the verified and checked life and key factor analytical expression, and the life value of the converter tube corresponding to each temperature is calculated; The life value is written back to the finite element model of the converter tube, which is used to obtain a life distribution cloud map of the converter tube, and a visual life prediction result is output.

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