Fatigue life prediction method for turbine blades based on logically constrained enhanced symbolic regression

Abstract

The invention discloses a method for predicting fatigue life of turbine blades based on logical constraint reinforced symbolic regression: construct a symbol library based on fatigue test data set of turbine blades; perform dimensionless preprocessing on input variables in the symbol library; construct a logical constraint reinforced symbolic regression model including a reinforcement learning module with RNN as carrier and a logical constraint rule module, select nodes from the symbol library to construct expressions, and select the expression with the best fitting effect as the fatigue life prediction formula based on the life determined by the real fatigue test; the reinforcement learning module guides the selection of nodes from the symbol library and the optimization of the constructed expression structure, and applies logical constraint rules in the selected nodes; obtain the basic mechanical performance parameters of the dangerous parts of the turbine blades under different working conditions as the input of the fatigue life prediction formula, output the fatigue life cycle number of the turbine blades under the corresponding working conditions, and realize the prediction of the fatigue life of the turbine blades. The method can improve its prediction efficiency and accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of fatigue life prediction of aircraft engine turbine blades, and in particular to a turbine blade fatigue life prediction method based on logical constraint enhanced symbolic regression. Background Art

[0002] As a key component in an aircraft engine, the fatigue life of turbine blades directly affects the safety and reliability of aircraft. The working environment of an aircraft engine has typical "three high" characteristics, namely high temperature, high pressure and high speed. The failure forms of blades are various, including fatigue failure, creep failure and high temperature damage. Among them, fatigue damage caused by alternating loads is one of the most common failure types of blade structures. Due to the complex failure mechanism of key components and tiny cracks, it is difficult to find defects such as tiny cracks on blades even through regular inspections. Therefore, the ability to conveniently and accurately predict the fatigue life of blades has gradually become the focus of attention in academia and industry. At present, there are many methods for predicting the fatigue life of blades. One of the widely used methods is to analyze the historical or real-time key parameters measured by sensors on blades, such as temperature, stress, strain and vibration. By performing time series prediction on these key parameters and combining them with failure cases, the time when the blade fails can be predicted. However, due to the lack of failure cases and data, researchers have gradually tried to accurately capture the intrinsic relationship between material mechanical properties (such as tensile strength, ductility, etc.) and fatigue properties in order to establish a more reliable fatigue life prediction model.

[0003] Traditional theoretical methods have derived a series of empirical formulas for establishing the relationship between mechanical properties and fatigue life, such as the Coffin-Manson equation, FS model, WHS model, etc. Although these empirical formulas have certain universality between different materials, they rely on a large amount of fatigue test data, are difficult to adapt to complex working conditions, and are difficult to obtain high-precision life predictions on specific materials. For example, the Chinese patent with publication number CN118013814A discloses a high-temperature air-cooled turbine blade life prediction method; including the following steps: S1, establish a reduced-order equation of the overall design parameters of the gas turbine and the blade temperature value and stress field through a deep learning algorithm; S2, obtain the actual temperature value and measured stress field of the blade corresponding to the actual operating condition of the gas turbine through sensors; S3, according to the measured temperature value and measured stress field obtained in step S2, modify the reduced-order equation in step S1; S4, calculate the blade temperature value and stress field based on the reduced-order equation modified in step S3, and predict the remaining life of the high-temperature gas-cooled turbine blade.

[0004] Data-driven machine learning algorithms provide new ideas for fatigue life prediction. Many studies have shown that powerful and flexible neural networks can accurately capture the influence trend between material mechanical performance parameters and fatigue life, and find the model parameters that best match the data set. However, neural networks are essentially "black box" models, which make it difficult to explain the physical meaning of parameters and their inherent influence mechanisms, and have poor interpretability. For example, the Chinese patent with publication number CN116701943A discloses a small sample turbine blade damage parameter prediction method based on meta-learning, which belongs to the field of turbine blade fatigue life assessment and prediction. Combined with the load characteristics of each typical position of the turbine blade during service, each typical position at different cross-sectional heights of the turbine blade is regarded as a different service task; a meta-learning model is used to effectively predict the damage parameters at each position of the turbine blade under different service times, improve blade utilization, and reduce the cost of use; in view of the problem that the service data of the turbine blade has typical time series correlation, but the time series is too short, the LSTM network is used as the base model, and the complete time series samples of each typical position are packaged as a "pseudo sample" to participate in model training, while using meta-learning to solve the small sample prediction problem and using the time series correlation of the sample to improve the prediction accuracy of the model.

[0005] In practical engineering, people prefer to use concise expressions that are easy to understand, generalizable, and can be linked to physical laws or known theories to reveal the intrinsic connections between data. Symbolic Regression (SR), as a model based on evolutionary algorithms, aims to generate interpretable and generalizable target expressions to describe the intrinsic connections between data. The generated explicit formula has the advantages of easy access and low computational cost, and shows great potential in applications that require understanding model behavior or following physical laws and concisely predicting future trends. Existing studies have shown that symbolic regression overcomes the shortcomings of insufficient prediction accuracy of empirical formulas and excessive reliance on prior knowledge. At the same time, compared with machine learning models, symbolic regression has higher interpretability and structural simplicity.

[0006] Therefore, how to improve the prediction accuracy by further improving the symbolic regression model is currently a research hotspot in this field. Summary of the invention

[0007] The purpose of the present invention is to provide a method for predicting the fatigue life of turbine blades based on logical constraint enhanced symbolic regression, which can realize the prediction of the fatigue life of turbine blades and improve its prediction efficiency and accuracy.

[0008] The present invention provides the following technical solutions:

[0009] A method for predicting fatigue life of turbine blades based on logical constraint enhanced symbolic regression, the method comprising the following steps:

[0010] S1: construct a symbol library based on a fatigue test data set of a turbine blade, wherein the symbol library includes the following nodes: input variables, operation operators and constants;

[0011] S2: perform dimensionless preprocessing on the input variables in the symbol library to obtain a preprocessed symbol library;

[0012] S3: construct a logical constraint reinforced symbolic regression model, including a reinforcement learning module based on RNN and a logical constraint rule module, which is used to select nodes from the preprocessed symbol library to construct a series of expressions, and take the life determined by the actual fatigue test as a benchmark, select the expression with the best fitting effect as the fatigue life prediction formula and then output it; wherein the reinforcement learning module based on RNN guides the selection of nodes from the symbol library and the optimization of the constructed expression structure, and applies logical constraint rules in the selected nodes through the logical constraint rule module;

[0013] S4: Perform finite element simulation on the turbine blade model to be tested to obtain basic mechanical performance parameters of dangerous parts of the turbine blade under different working conditions, which are used as input of the fatigue life prediction formula output by step S3, and the fatigue life cycle number of the turbine blade under the corresponding working condition is output to realize the prediction of the fatigue life of the turbine blade.

[0014] The technical concept of the present invention is: for the fatigue life prediction of aircraft engine turbine blades, the present invention builds a reinforcement learning guided expression for directed generation, and combines logical constraint rules to reduce the search space and ensure the physical logical rationality of the expression. The model specifically includes: a symbol library as a symbol node search space, a reinforcement learning module with RNN as the carrier, and logical constraint rules. Each expression is equivalent to a separate binary tree structure, in which each symbol node comes from the symbol library; the reinforcement learning module generates a selection probability for the symbol in the symbol library according to the current expression state, and selects new nodes to add expressions in combination with the probability of logical constraint rules, thereby constructing a series of complete expressions. A certain proportion of excellent expressions and corresponding feedback reward values ​​are selected from the constructed expressions for training the RNN network, so that the RNN can learn excellent structures and improve learning strategies. Until finally, an excellent expression that matches the real data set is spontaneously generated as a fatigue life prediction formula for blade materials.

[0015] In step S1, the input variables are basic mechanical performance parameters of turbine blades, including: axial stress , shear stress , Young's modulus E, shear modulus G, axial strain rate and shear strain rate The operation operators include addition operator, subtraction operator, multiplication operator, division operator, trigonometric operator, and exp exponential operator. The symbol library serves as the search space for nodes in the subsequent model construction expression process.

[0016] In step S2, considering that the input mechanical property parameters usually have physical units, such as MPa, GPa, etc., in order to unify the physical units on both sides of the expression, the present invention performs dimensionless preprocessing on the input variables in the symbol library according to the physical unit dimension and empirical formula method, thereby converting the input variables with physical units into a combination structure with actual physical meaning and no physical units; the specific method is: symbolic operations are performed between the input variables with physical units, and the input variables are converted into dimensionless preprocessing after dimensionless preprocessing. , , and .

[0017] In step S3, the reinforcement learning module based on RNN uses RNN to guide node selection and expression structure optimization, specifically: RNN generates the selection probability of each node in the symbol library as the selection strategy of reinforcement learning, and each selection behavior has a corresponding feedback reward value, which is related to the fitting effect of the expression; RNN generates a batch of expressions, selects excellent expressions from them and strengthens the selection behaviors related to high reward values, guiding subsequent batches to generate better expressions, and the iterative process continues until RNN can autonomously select suitable nodes from the symbol library according to the expression state, and the logical constraint reinforcement symbolic regression model can generate the expression with the best fitting effect.

[0018] The present invention proposes to use reinforcement learning to train RNN network parameters and guide the selection process of nodes in the expression, so as to generate an expression that accurately matches the data set. From each batch of expressions generated, the excellent expression with the lowest RMSE and the best fitting effect is selected, and the actions related to the high feedback reward value in the excellent expression are further strengthened, and finally an expression with excellent fitting effect is generated. By comparing with the empirical formula method and the typical machine learning method, the method proposed in the present invention achieves equivalent or even better prediction accuracy, and obtains the explicit prediction formula of fatigue life, which is convenient for combination with physical laws and theories.

[0019] Or it can be understood as using reinforcement learning strategies to guide the model to select nodes. RNN, as a reinforcement learning carrier, generates selection probabilities for the symbol library nodes according to the context of the expression, selects some excellent expressions from each batch of expressions to train the RNN network parameters, and strengthens the excellent structure with the goal of maximizing feedback rewards, encouraging the generation of excellent expressions in the next batch.

[0020] In step S3, the logical constraint rules in the logical constraint rule module specifically include: arrays (such as "arity" arrays) tracking expression construction, controlling expression length, and strict constraints on constant operations and function nesting; wherein, the logical constraint rules are applied to the selection process of each node in the form of selection probability, and the node type that violates the rule is imposed with a negative infinite selection probability; and the L-BFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) optimization algorithm is applied to determine the optimal value of the constant node.

[0021] The present invention applies logical constraint rules, reduces the node search space and optimizes the expression structure and rationality, so as to improve the structural simplicity and rigor of the generated formula and ensure the expression structure and logical validity.

[0022] The array tracking expression construction is specifically as follows: the expression adopts a binary tree structure, and uses an initially blank array to track the hanging status of tree structure nodes. For each additional operation operator node, the number of child nodes that need to be hung is placed in the array; for each additional input variable or constant node, the number of child nodes at the end of the array is reduced by one, and this is repeated until the array is empty, and the expression construction is completed;

[0023] The controlling expression length specifically includes: constraining the expression length by limiting the number of operation operator nodes;

[0024] The strict constraints on constant operations are specifically: constraining the number of constant nodes by the complexity of the data set and limiting meaningless constant operations;

[0025] The strict constraints on function nesting are specifically: constraining the nesting operation of unary functions.

[0026] In step S3, the logic constraint enhanced symbolic regression model directly outputs the optimal fatigue life prediction formula of different materials of turbine blades under different working conditions;

[0027] Alternatively, the logic constraint enhanced symbolic regression model outputs the optimal fatigue life prediction formula for different materials under a certain working condition, and then for turbine blades with the same material, the fatigue life prediction formula is used as a general structural expression, and the constant nodes in the expression are explored and adjusted to obtain the optimal fatigue life prediction formula for the turbine blade material under different working conditions.

[0028] It should be noted that different materials can be in the same working condition or in different working conditions under a certain working condition without limitation. For turbine blades with the same material, the fatigue life prediction formulas corresponding to different working conditions are structurally universal; therefore, by retaining the formula structure of the optimal fatigue life prediction formula under a certain working condition and exploring the optimal constant values ​​for other working conditions, the fatigue life prediction formula of the turbine blade material under different working conditions can be obtained.

[0029] Furthermore, the output of the logical constraint enhanced symbolic regression model is a fatigue life prediction formula for different materials under a certain working condition. The fatigue test data sets of GH4169 and TC4, commonly used materials for turbine blades, are applied to the prediction method provided by the present invention to obtain the fatigue life general prediction formula for turbine blades made of GH4169 and TC4 materials, which is as follows:

[0030] General formula for GH4169 material under different working conditions:

[0031] ;

[0032] General formula for TC4 material under different working conditions:

[0033] ;

[0034] in , , , , , , , , They all represent constant values ​​in general formulas and vary with different operating conditions.

[0035] Furthermore, in step S4, a finite element simulation can be performed on the turbine blade model based on COMSOL simulation software to simulate the forces acting on the blade under operating conditions, thereby predicting the fatigue life of the blade under corresponding conditions.

[0036] The present invention also provides a turbine blade fatigue life prediction device based on logical constraint enhanced symbolic regression, comprising a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the above-mentioned turbine blade fatigue life prediction method based on logical constraint enhanced symbolic regression.

[0037] The present invention also provides a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the above-mentioned turbine blade fatigue life prediction method based on logical constraint enhanced symbolic regression.

[0038] Compared with the prior art, the present invention has the following excellent effects:

[0039] (i) Introducing logical constraints: The present invention imposes logical constraint rules in the symbolic regression algorithm, significantly optimizing the node search space and ensuring the rationality of the generated expression structure and its conformity to the actual physical meaning;

[0040] (ii) Using deep reinforcement learning to strengthen excellent expressions: The present invention proposes to use reinforcement learning guidance based on RNN in the training of node selection strategy, continuously strengthen the generation of excellent structures, and improve the efficiency and accuracy of high-quality expression generation;

[0041] (III) Superior application performance: The prediction method provided by the present invention can obtain an explicit expression between the mechanical properties and fatigue properties of the material, thereby effectively predicting the fatigue life cycles of the blade under different working conditions. Compared with the traditional empirical formula method and machine learning model, the present invention shows better prediction accuracy and interpretability;

[0042] (IV) The prediction method provided by the present invention captures the intrinsic connection between the mechanical properties of materials and fatigue life, and finds that the structure of the fatigue life prediction formula corresponding to the same material under different working conditions is universal. Therefore, as an implementable method, the prediction efficiency of the fatigue life of materials under different working conditions can be improved by proposing a universal formula, while reducing the node search space in the process of constructing the prediction formula.

[0043] As fatigue data sets continue to expand in the future, combining the method proposed in this invention with finite element simulation can provide a reliable reference for life prediction and maintenance and repair of key components in future engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic diagram of the application principle of the logical constraint enhanced symbolic regression model proposed in the present invention;

[0045] Figure 2 A comparison chart of the material fatigue life prediction value and the actual value obtained by the GH4169 optimal life prediction formula at 25°C in the present invention;

[0046] Figure 3 It is a comparison chart of the material fatigue life prediction value and the actual value obtained by the optimal life prediction formula of GH4169 at 650°C in the present invention;

[0047] Figure 4 This is a comparison chart of the material fatigue life prediction and true value obtained by the enhanced symbolic regression algorithm using the GH4169 validation data set at 25°C in the ten-fold cross validation method;

[0048] Figure 5This is a comparison chart of the material fatigue life prediction and true value obtained by strengthening the symbolic regression algorithm using the GH4169 validation data set at 650°C in the ten-fold cross validation method;

[0049] Figure 6 This is a comparison chart of the fatigue life prediction and actual value of GH4169 obtained by the Coffin Manson equation in the empirical formula;

[0050] Figure 7 This is a comparison chart of the fatigue life prediction value and the actual value of GH4169 obtained by BM in the empirical formula;

[0051] Figure 8 This is a comparison chart of the fatigue life prediction value and the actual value of GH4169 obtained by KBM in the empirical formula;

[0052] Fig. 9 This is a comparison chart of the fatigue life prediction value and the actual value of GH4169 obtained by FS in the empirical formula;

[0053] Fig.10 This is a comparison chart of the fatigue life prediction and actual value of GH4169 obtained by WHS in the empirical formula;

[0054] Fig.11 This is a comparison chart of the fatigue life prediction value and the actual value of GH4169 obtained by MWHS in the empirical formula;

[0055] Fig.12 This is a comparison chart of the fatigue life prediction value and the actual value of GH4169 obtained by the enhanced symbolic regression algorithm proposed in the present invention;

[0056] Fig.13 This is a comparison chart of the fatigue life prediction and true value of GH4169 obtained by LSTM in the machine learning model;

[0057] Fig.14 This is a comparison chart of the fatigue life prediction and true value of GH4169 obtained by SVR in the machine learning model;

[0058] Fig.15 This is a comparison chart of the fatigue life prediction and true value of GH4169 obtained by RF in the machine learning model;

[0059] Fig.16 This is a comparison chart of the fatigue life prediction and true value of GH4169 obtained by Gradient Boosting in the machine learning model;

[0060] Fig.17 This is a comparison chart of the GH4169 fatigue life prediction and true value obtained by XGBoost in the machine learning model. DETAILED DESCRIPTION

[0061] Here, the implementation examples will be described in detail, and the specific example results will be shown in the accompanying drawings. The terms used in the present invention are only for describing specific implementation examples and are not intended to limit the present invention.

[0062] The turbine blade fatigue life prediction method (RSL) based on logical constraint enhanced symbolic regression proposed in the present invention is used to establish fatigue life prediction formulas for common turbine blade materials GH4169 and TC4, and predict blade fatigue life, thereby confirming the performance advantage of the method of the present invention. The specific implementation of the present invention is described more completely and clearly in conjunction with the accompanying drawings, which specifically includes the following steps.

[0063] Step 1: Determine the data set and symbol library;

[0064] Step 1.1, obtaining a turbine blade material fatigue test data set according to a turbine blade material fatigue test, which includes a true life value of the material;

[0065] Step 1.2, determine the symbol library and output of the logical constraint enhanced symbolic regression model based on the turbine blade material fatigue test data set; the symbol library includes the following nodes: input variables, operation operators and constants; let the input variables is the basic mechanical properties parameter of the material, that is , specifically the axial strain of the material , shear strain , axial stress , shear stress , Young's modulus , shear modulus ; The output of the logical constraint enhanced symbolic regression model is the fatigue life prediction formula; Determine the operation operators involved in the model, mainly including binary operation operators and the unary operator , where the number of child nodes for binary operators is 2, and the number of child nodes for unary operators is 1. The symbol library is represented as ,in Represents the basic mechanical properties parameters of the input material, Represents all the operators. Represents a constant node in an expression. Expression sequence nodes are all sampled from the symbol library.

[0066] Step 2: Perform dimensionless preprocessing on the input variables;

[0067] Considering that the input mechanical properties usually have physical units, such as MPa, GPa, etc., in order to unify the physical units on both sides of the expression, the present invention introduces dimensionless preprocessing to convert the input variables with physical units into a dimensionless variable combination structure that retains the actual physical meaning. Instead of inputting the axial stress ,use Replace shear stress In the stress-strain curve, Corresponding to the slope, this means Physically represents the axial strain, similarly, represents the shear strain.

[0068] Step 3: Obtain the material fatigue life prediction formula based on the logical constraint strengthening symbolic regression model;

[0069] like Figure 1 As shown, a logical constraint reinforced symbolic regression model is constructed, nodes are selected from the preprocessed symbol library to construct a series of expressions, and the life determined by the actual fatigue test is used as a benchmark, and the expression with the best fitting effect is selected as the optimal fatigue life prediction formula and then output; wherein the logical constraint reinforced symbolic regression model includes a reinforcement learning module with RNN as the carrier and a logical constraint rule module, wherein the reinforcement learning module with RNN as the carrier guides the selection of nodes in the symbol library, and applies logical constraint rules in the selected nodes through the logical constraint rule module;

[0070] The logical constraint enhanced symbolic regression model adds logical constraint rules to the selection of nodes in the expression, narrows the node search space, optimizes the expression structure, and ensures the rationality of physical meaning. The logical constraint rules include:

[0071] (1) Update the "arity" array to track the progress of expression construction and ensure that the expression is fully constructed: Use a binary tree structure to represent the expression. When constructing the tree structure of the expression, introduce an initially empty "arity" array. This array is continuously updated corresponding to the expression status, reflecting the number of child nodes required for each operator node in the tree structure; specifically, when a new operator node is introduced, the number of child nodes required for the operator node will be added to the end of the "arity" array; when adding a constant node or input variable node, the end value in the array is reduced by one; when the end value is zero, it is removed, and the new end value is reduced by one. This step is repeated until the array is a blank array, indicating that the expression is fully constructed;

[0072] (2) Controlling the length of expression by the number of operator nodes: The present invention takes into account the diversity of expression forms. The model generates operator nodes and constant nodes alternately, which may cause the expression tree to be fully constructed before reaching the specified length. To avoid this situation, the present invention proposes that if the operator node has not reached the preset length value, the "arity" array is set to all 1, and the operator node is forced to be selected as the next new node;

[0073] (3) Constant operation suppression mechanism: In most cases, the result of a constant operation can be replaced by a constant value. Considering the simplicity of expressions, the present invention prohibits all child nodes under an operation operator node from being constants, such as in the form of etc. At the same time, the number of constant nodes has a significant impact on the expression structure. If the number is not limited, the algorithm will often over-explore constants to replace variable parameters. Therefore, the present invention sets a threshold for the number of constant nodes, which can be adjusted according to the length of the expression definition and the complexity of the data set.

[0074] (4) Function nesting control: In actual physical formulas, the nested structure of univariate functions is rare and usually has no actual physical meaning. In terms of computing performance, the continuous nesting of function operations will lead to a significant expansion of the computing space, especially exponential nesting. At the same time, in order to avoid redundant and meaningless function inverse operations that affect simplicity, the present invention limits the nested operations of univariate functions.

[0075] In order to improve the efficiency of generating effective expressions, the present invention applies constraint rules to the selection process of each node. In the selection probability of each node generated by RNN, nodes that violate the constraint rules are assigned a negative infinite probability, and the two are combined to select a suitable new node.

[0076] The logical constraint reinforced symbolic regression model uses reinforcement learning strategy to train the network to select nodes. RNN is the core of node selection, which generates distribution probabilities for nodes in the symbol library as a selection strategy in reinforcement learning. In reinforcement learning, the action is selected according to the current expression state by the policy function Decide: ;

[0077] in Corresponding to the current expression status; Represents the behavior of selecting the next node from the symbol library; Represents the weight parameters of the RNN network, which are optimized through training. Selecting nodes according to the policy function will generate corresponding action rewards. The expected cumulative reward under a given policy can be expressed as the state value function It is described by the Bellman Expectation Equation as:

[0078] ;

[0079] in Is to perform an action The next state after that, the expected reward for the next state Discount factor for current impact measure, Yes Status Next action The corresponding immediate reward. State-action value function Indicates in status Next select action Expected cumulative reward after:

[0080] ;

[0081] The Q function can be used to evaluate the quality of each action and guide policy optimization. To select nodes more accurately, Parameters in Optimize. The optimization process is achieved through policy gradient, by maximizing the expected reward To update the policy:

[0082] ;

[0083] in, represents the gradient, is the log probability of the policy function, whose gradient is used to adjust the parameters , in order to enhance the probability of selecting high reward actions. In the present invention, the prediction accuracy of the expression is expressed by the mean square error RMSE and the determination coefficient between the predicted life value and the actual life value. The feedback reward for node selection is defined as the negative RMSE value, which encourages the expression to be generated in the direction of decreasing the RMSE value. When training the network parameters, the excellent expression with the lowest RMSE and the best fitting effect is selected in each batch of generated expressions, and then used to strengthen the excellent structure. Among them, the calculation method of the predicted life value is: the basic mechanical performance parameters of the turbine blade material are input into the corresponding expression for calculation.

[0084] There is no observable state for the selection of the first node of an expression. The present invention counts the types and occurrence probabilities of the first nodes in the previous batch of excellent expressions, introduces certain variations, and selects the first node of the expression in the current batch accordingly, so that the generation of all nodes has a reference strategy.

[0085] In order to determine the constant node value, the present invention uses the L-BFGS optimization algorithm to optimize the constant value and find the optimal constant value that minimizes the expression fitting error. The L-BFGS gradient descent formula is:

[0086] ;

[0087] in, represents the true fatigue life in the test data set, represents the fatigue life predicted by the expression, It represents the optimal constant value that minimizes the RMSE between the true value and the predicted value of fatigue life.

[0088] The fatigue test datasets of GH4169 and TC4, common materials for turbine blades, were input into the above-mentioned logical constraint enhanced symbolic regression model. The expression structure constraint hyperparameters set according to the complexity of the reference dataset are shown in Table 1, which restricts the overall structural characteristics such as the expression length.

[0089] In this embodiment, the source of the turbine blade material fatigue test data set is:

[0090] Wu ZR, HU XT, SONG YD. Multiaxial fatigue life prediction for titanium alloy TC4 under proportional and nonproportional loading [J]. International Journal of Fatigue, 2014, 59: 170-5.

[0091] Wu et al., Evaluation of multiaxial fatigue life prediction criteria for nickel-based superalloy GH4169 [J], Transactions of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2017, 232:095440621770821 (WU ZR, HU XT, SONG YD. Multiaxial fatigue life prediction for titanium alloy TC4 under proportionaland nonproportional loading [J]. International Journal of Fatigue, 2014, 59:170-5.);

[0092] SUN GQ, SHANG DG, BAO M. Multiaxial fatigue damage parameter and life prediction under low cycle loading for GH4169 alloyand other structural materials [J]. International Journal of Fatigue, 2010, 32(7): 1108-15.

[0093] Table 1 Expression overall structure constraint hyperparameter settings

[0094] ;

[0095] in, Indicates the number of expressions generated in each batch, Indicates the batch number, The number of batches representing the number of expanded expressions, represents the proportion of excellent expressions in the initial expansion batch, Indicates the proportion of excellent expressions in subsequent batches. The present invention expands the number of expressions in the initial two batches from 1300 to 16900 to make the forms more diversified. Indicates the length of the expression, Represents the maximum number of constants in an expression. These hyperparameters provide structural constraints for expressions and limit the complexity of expressions. They can be adjusted based on the complexity and size of the dataset.

[0096] The present invention uses RMSE and determination coefficient As a performance evaluation criterion, RMSE is a measure of the difference between the observed value and the true value. The smaller the value, the higher the prediction accuracy; The range is [0,1]. The closer to 0, the worse the fit between the model and the data, and the closer to 1, the better the fit.

[0097] As the first implementation method: the output of the logical constraint enhanced symbolic regression model is the fatigue life prediction formula of different materials of turbine blades under different working conditions. Under the structural constraint hyperparameters set in Table 1, the representative excellent fatigue life prediction formula output by adjusting the RNN model training intensity is shown in Table 2, where is the number of fatigue life cycles.

[0098] Table 2 Representative excellent expressions

[0099] ;

[0100] It can be seen from Table 2 that under the hyperparameters set in Table 1, the optimal fatigue life prediction formula for GH4169 at 25°C is (1), the optimal fatigue life prediction formula for GH4169 at 650°C is (7), and the optimal fatigue life prediction formula for TC4 at 25°C is (4).

[0101] As the second implementation method, the output of the logical constraint enhanced symbolic regression model is the optimal fatigue life prediction formula for different materials under a certain working condition. Then, for turbine blades with the same material, the fatigue life prediction formula is used as a general structural expression. The specific structure of the expression is retained and the optimal value of the constant node in the expression is explored and adjusted to obtain the fatigue life prediction formula for this type of turbine blade material under different working conditions.

[0102] Specifically, referring to the previous implementation, for GH4169, only the fatigue test data set of GH4169 at 25°C is used as input, and the representative excellent expressions (1)-(3) of GH4169 at 25°C in Table 2 are output. Then, RMSE and determination coefficient are used to calculate the As the performance evaluation standard, the expression (1) with the best fitting effect of GH4169 at 25°C is selected as the fatigue life prediction formula of the material under this working condition:

[0103] ;

[0104] Keep its structure as the general fatigue life prediction formula for GH4169 material:

[0105] ;

[0106] in, , , , , They all represent constant values ​​in the general formula and change with different working conditions. The L-BFGS optimization algorithm is used in the model to explore the optimal constant values ​​of the expression under different working conditions, and the fatigue life prediction formula of GH4169 at 650°C is obtained:

[0107] ;

[0108] The RMSE value between the fatigue life predicted by the above fatigue life prediction formula and the actual fatigue life is , The value is 0.96022. The comparison between the predicted value and the true value is as follows Figure 2 and Figure 3As shown. At 25℃, all GH4169 material sample points fall within the 3-fold error band, and 94.4% of the material sample points fall within the 2-fold error band; at 650℃, all GH4169 material sample points fall within the 3-fold error band, and 88.9% of the material sample points fall within the 2-fold error band; the results show that the prediction accuracy of the fatigue life prediction formula at 650℃ explored by this method has reached a satisfactory prediction level, that is, the prediction effect of the fatigue life prediction expression corresponding to different working conditions explored by retaining the general expression structure is excellent.

[0109] From the above fatigue life prediction formula examples, it can be found that the fatigue life prediction formulas corresponding to the same material under different working conditions are universal in structure. After obtaining the optimal prediction formula of GH4169 under a certain working condition, its structure can be retained, and the expression constant values ​​under different working conditions can be explored to obtain the fatigue life prediction formulas corresponding to different working conditions.

[0110] As shown above, the general formula for TC4 material under different working conditions is:

[0111] ;

[0112] in, , , , They all represent constant values ​​in general formulas and vary with different operating conditions.

[0113] In order to prevent the proposed algorithm from overfitting in the application of exploring the general expression structure, the present invention uses a ten-fold cross-validation method to evaluate the generalization ability of the model on the material data to ensure the robustness and reliability of the model. The GH4169 data set at 25°C is divided into ten parts, and each part is used as a validation set to train the model, and the training set is used to explore the general structure of the expression. The results of the ten validation evaluations are integrated, as shown in Figure 4 and Figure 5 It is found that the trend observed in the ten validation results is consistent with Figure 2 and Figure 3 For GH4169 at 25°C, more than 90% of the predicted data are within the 2-fold error band, and the RMSE value is This shows that the generalization ability of this algorithm is robust and can effectively predict unknown data.

[0114] Furthermore, the optimal fatigue life prediction formula of GH4169 at 25°C in the second implementation and the fatigue life prediction formula at 650°C explored from the general structure were compared with six empirical formulas and five commonly used machine learning algorithms to verify the model performance. The comparison with empirical formulas includes Coffin Manson equation, BM (Brown-Miller) and KBM (Kandil, Brown and Miller) models, FS (Fatemi and Socie) model, WHS and MWHS models. The comparison results are as follows: Figure 6-Figure 12 Among all algorithms, the RMSE and The value works best and has the best prediction accuracy.

[0115] Compared with machine learning algorithms, including Long Short-Term Memory (LSTM), Support Vector Regression (SVR), Random Forest (RF), Gradient Boosting, and XGBoost, the comparison results are as follows Figure 13-Figure 17 As shown. Among the algorithms involved in the comparison, the fatigue life prediction formula proposed by the present invention ( Fig.12 ) has achieved prediction accuracy comparable to or even better than that of machine learning algorithms. Compared with black box models such as machine learning algorithms, the method proposed in this invention is interpretable and more generalizable in a physical context.

[0116] Step 4: Predict turbine blade fatigue life

[0117] Considering the working environment of turbine blades, the material parameters of GH4169 at 650 °C were applied to a single blade model for COMSOL finite element simulation. The centrifugal force simulated by the cyclically symmetrical speed change and the blade's own gravity were applied to obtain the basic mechanical performance parameters of the dangerous parts of the blade under different speed conditions, as shown in Table 3.

[0118] Table 3 Basic mechanical properties of dangerous parts of blades under different working conditions

[0119] ;

[0120] The basic mechanical properties parameters at the dangerous parts of the blade are used as the optimal prediction expression (7) of GH4169 material at 650°C in step 3 and the second implementation method, that is, the prediction expression explored by the general structure, to predict the number of fatigue life cycles of the blade under the corresponding working conditions. The WHS model with excellent performance in step 3 is used as the representative method of the empirical formula. The prediction results of the three methods are shown in Table 4. It can be seen from the results that under the working conditions of S3 and S4, the expression obtained by using the general structure exploration predicts the life value ( ) and the optimal prediction expression predicts the life value ( ), further confirming the reliability of the general structure; the fatigue life predicted by the empirical formula represented by WHS and the logical constraint enhanced symbolic regression model is consistent in dimension and has little difference, and the change trend is consistent. Under cyclic symmetrical speed load, the greater the change in the working conditions of the turbine blades, the shorter their fatigue life will be.

[0121] Table 4 Prediction results of blade fatigue life under different working conditions by enhanced symbolic regression model and WHS

[0122] ;

[0123] Through the above example analysis, combined with the comparison results with the empirical formula method and the machine learning model, the main technical contributions of the present invention are: a turbine blade fatigue life prediction method based on logical constraint enhanced symbolic regression is proposed, and the prediction method is based on a new symbolic regression model guided by deep reinforcement learning and with logical constraint rules (i.e., logical constraint enhanced symbolic regression model); the present invention proposes the application of logical constraint rules to optimize the node search space and ensure the rationality of the generated expression structure and the effectiveness of the actual physical meaning; it proposes to use reinforcement learning guidance with RNN as the carrier in the training of node selection strategy to improve the efficiency and accuracy of generating high-quality expressions.

[0124] As fatigue test data sets continue to expand in the future and finite element simulation results continue to approach the actual fatigue failure form, combining the algorithm proposed in this invention with finite element simulation can provide a reliable reference for life prediction and maintenance and repair of key components in future engineering applications.

[0125] The above specification and description of the implementation examples are used to explain the scope of protection of the present application, but are only for illustrative purposes and are not restrictive to the scope of application of the present invention. Any changes made without departing from the spirit of the invention and the scope of protection of the claims shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting fatigue life of turbine blades based on logical constraint enhanced symbolic regression, characterized in that: The method comprises the following steps: S1: construct a symbol library based on a fatigue test data set of a turbine blade, wherein the symbol library includes the following nodes: input variables, operation operators and constants; S2: perform dimensionless preprocessing on the input variables in the symbol library to obtain a preprocessed symbol library; S3: construct a logical constraint reinforced symbolic regression model, including a reinforcement learning module based on RNN and a logical constraint rule module, which is used to select nodes from the preprocessed symbol library to construct a series of expressions, and take the life determined by the actual fatigue test as a benchmark, select the expression with the best fitting effect as the fatigue life prediction formula and then output it; wherein the reinforcement learning module based on RNN guides the selection of nodes from the symbol library and the optimization of the constructed expression structure, and applies logical constraint rules in the selected nodes through the logical constraint rule module; S4: Perform finite element simulation on the turbine blade model to be tested to obtain basic mechanical performance parameters of dangerous parts of the turbine blade under different working conditions, which are used as inputs of the fatigue life prediction formula output in step S3, and the fatigue life cycle number of the turbine blade under the corresponding working conditions is output to achieve the prediction of the fatigue life of the turbine blade; In step S1, the input variables are basic mechanical performance parameters of turbine blades, specifically including: axial stress σ a , shear stress τ a , Young's modulus E, shear modulus G, axial strain rate ε a and the shear strain rate γ a ; The operation operators include addition operator, subtraction operator, multiplication operator, division operator, trigonometric function operator, exp exponential operator; In step S3, the reinforcement learning module based on RNN uses RNN to guide node selection and expression structure optimization, specifically: RNN generates the selection probability of each node in the symbol library as the selection strategy of reinforcement learning, and each selection behavior has a corresponding feedback reward value, which is related to the fitting effect of the expression; RNN generates a batch of expressions, selects excellent expressions from them and strengthens the selection behaviors related to high reward values, and guides subsequent batches to generate better expressions, which continues until RNN can autonomously select appropriate nodes from the symbol library according to the expression state, and the logical constraint reinforcement symbol regression model can generate the expression with the best fitting effect; In step S3, the logical constraint rules in the logical constraint rule module specifically include: using array tracking expression construction, controlling expression length, and strict constraints on constant operations and function nesting; wherein, the logical constraint rules are applied to the selection process of each node in the form of selection probability, and a negative infinite selection probability is applied to the node type that violates the rule; and the L-BFGS optimization algorithm is applied to determine the optimal value of the constant node.

2. The method for predicting turbine blade fatigue life based on logical constraint enhanced symbolic regression according to claim 1, characterized in that: In step S2, the input variables in the symbol library are dimensionlessly preprocessed. The specific method is: symbolic operations are performed between input variables with physical units, and the input variables are converted into σ after dimensionless preprocessing. a / E, τ a / G,ε a and γ a .

3. The method for predicting turbine blade fatigue life based on logical constraint enhanced symbolic regression according to claim 1, characterized in that: The array tracking expression construction is specifically as follows: the expression adopts a binary tree structure, and uses an initially blank array to track the hanging status of tree structure nodes. For each additional operation operator node, the number of child nodes that need to be hung is placed in the array; for each additional input variable or constant node, the number of child nodes at the end of the array is reduced by one, and this is repeated until the array is empty, and the expression construction is completed; The controlling expression length specifically includes: constraining the expression length by limiting the number of operation operator nodes; The strict constraints on constant operations are specifically: constraining the number of constant nodes by the complexity of the data set and limiting meaningless constant operations; The strict constraints on function nesting are specifically: constraining the nesting operation of unary functions.

4. The method for predicting turbine blade fatigue life based on logical constraint enhanced symbolic regression according to claim 1, characterized in that: In step S3, the output of the logic constraint enhanced symbolic regression model is a fatigue life prediction formula for different materials of turbine blades under different working conditions; Alternatively, the output of the logical constraint enhanced symbolic regression model is a fatigue life prediction formula for different materials under a certain working condition. Then, for turbine blades with the same material, the fatigue life prediction formula for different materials under a certain working condition is used as a general structural expression, and the constant nodes in the expression are explored and adjusted to obtain the fatigue life prediction formula for the turbine blade material under different working conditions.

5. The method for predicting turbine blade fatigue life based on logical constraint enhanced symbolic regression according to claim 4, characterized in that: The output of the logical constraint enhanced symbolic regression model is the fatigue life prediction formula of different materials under a certain working condition. For turbine blades made of GH4169 material and TC4 material, the fatigue life prediction formula is as follows: General formula for GH4169 material under different working conditions: General formula for TC4 material under different working conditions: Among them, a, b, c, d, e, a ′ , b ′ , c ′ , d ′ They all represent constant values ​​in general formulas and vary with different operating conditions.

6. A turbine blade fatigue life prediction device based on logical constraint enhanced symbolic regression, characterized in that: It comprises a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, it is used to implement the turbine blade fatigue life prediction method based on logical constraint enhanced symbolic regression as described in any one of claims 1-5.

7. A computer-readable storage medium having a program stored thereon, which, when executed by a processor, is used to implement the turbine blade fatigue life prediction method based on logical constraint enhanced symbolic regression as described in any one of claims 1 to 5.

Images