US-20260127337-A1 - FATIGUE LIFE PREDICTION METHOD OF TURBINE BLADE BASED ON LOGIC CONSTRAINT-ENHANCED SYMBOLIC REGRESSION

US20260127337A1US 20260127337 A1US20260127337 A1US 20260127337A1US-20260127337-A1

Abstract

A fatigue life prediction method of a turbine blade based on logic constraint-enhanced symbolic regression, includes: constructing a symbol library based on a turbine blade fatigue test dataset; performing dimensionless preprocessing on input variables in the library; constructing a logic constraint-enhanced symbolic regression model with a reinforcement learning module with an RNN as a carrier and a logic constraint rule module, selecting a node from the library to construct expressions, and selecting an expression with best fitting effect as a prediction formula by using a real fatigue test benchmark; guiding the node selection and optimization of the constructed expression structure, and applying a logic constraint rule in the selected node; and obtaining basic mechanical property parameters of a dangerous part under different working conditions, which are used as an input of the fatigue life prediction formula, and outputting a fatigue life cycle number to predict turbine blade fatigue life.

Inventors

Yiming Zhang
Pei Li
Shuyou ZHANG

Assignees

ZHEJIANG UNIVERSITY

Dates

Publication Date: 20260507
Application Date: 20250521
Priority Date: 20241104

Claims (6)

1 . A computer-implemented method for predicting fatigue life of a turbine blade based on logic constraint-enhanced symbolic regression, wherein the method comprises the following steps: S 1 : obtaining a turbine blade material fatigue test dataset including a true life value of the turbine blade material based on a turbine blade material fatigue test; constructing a symbol library based on the fatigue test dataset of the turbine blade, wherein the symbol library comprises nodes, the nodes comprising: input variables, arithmetic operators, and constants; the input variables are basic mechanical property parameters of the turbine blade, comprising: axial stress σ a , shear stress τ a , Young's modulus E, shear modulus G, an axial strain rate ε a , and a shear strain rate γ a ; and the arithmetic operators comprising an addition operator, a subtraction operator, a multiplication operator, a division operator, a trigonometric function operator, and an exponential operator; S 2 : performing dimensionless preprocessing on the input variables in the symbol library to obtain a preprocessed symbol library; S 3 : selecting a node from the preprocessed symbol library to construct a series of expressions; and selecting an expression from the series of expressions, and outputting the selected expression with a fitting effect that is closest to a real fatigue test as a fatigue life prediction formula by obtaining a second fatigue life determined by the real fatigue test as a benchmark, wherein the selection of the node is guided by reinforcement learning with a recurrent neural network (RNN) as a carrier guides the selection of the node from the symbol library and optimization of the structure of the series of expressions, and applies a logic constraint rule in the selected node; wherein the RNN generates a selection probability of each node in the symbol library as a selection strategy of reinforcement learning, and each selection behavior has a corresponding feedback reward value, which is related to a fitting effect of the expression; and the RNN generates the series of expressions, selects a first expression therefrom, reinforces a selection behavior related to a higher reward value than the corresponding feedback reward value of the selection behavior of the selection of the first expression, and guides subsequent series to generate second expressions; the selection process continues until the RNN independently select an appropriate node from the symbol library according to an expression state, and the RNN generates the expression with the fitting effect that is closest to the real fatigue test; and wherein the logic constraint rule comprises: tracking the construction of the expressions by using an array, controlling a length of the expressions, and imposing a constraint on a constant operation and function nesting, wherein the logic constraint rule is applied to the selection process of each node in a form of the selection probability, and a negative infinite selection probability is applied to a node type that violates the rule; and an optimal value of a constant node is determined by using limited-memory Broyden Fletcher-Goldfarb-Shanno optimization; and S 4 : performing a finite element simulation on a turbine blade model to be tested by applying cyclically symmetrically varying rotational speed to simulate centrifugal force and the blade's own weight to obtain basic mechanical property parameters of another part of the turbine blade under different working conditions, which are used as an input of the fatigue life prediction formula output in step S 3 , and outputting a fatigue life cycle number of the turbine blade under a corresponding working condition, so as to realize prediction of the fatigue life of the turbine blade; wherein in the step S 3 , the output of the RNN is the fatigue life prediction formulas for turbine blade made of different materials under different working conditions, or the output of the RNN is the fatigue life prediction formulas for different materials under a certain working condition; and then for turbine blades made of the same material, by taking the fatigue life prediction formulas for the different materials under the certain working condition as general structural expressions, and exploring and adjusting the constant nodes in the expressions; wherein the output of the RNN is the fatigue life prediction formulas for different materials under the certain working condition, and for turbine blades made of GH4169 material and TC4 material, fatigue life prediction formulas are as follows: a first general formula for the GH4169 material under different working conditions: ln ⁡ ( N f ) = a + b ⁡ ( ε a ⁢ τ a G + c ⁢ τ a G + d ) ( ε a + γ a ) ⁢ ( ε a ⁢ τ a G + c ⁢ τ a G + d ) + e a second general formula for the TC4 material under different working conditions: ln ⁡ ( N f ) = a ′ + b ′ ( ε a c ′ - τ a G + σ a E ) + d ′ ε a wherein a, b, c, d, e, a′, b′, c′, and d′ all represent constant values in the first and second general formulas, which vary with different working conditions; σ a /E physically represents the axial strain, τ a /G represents the shear strain, N f is the number of fatigue life cycles.
2 . The method according to claim 1 , wherein in the step S 2 , performing dimensionless preprocessing on the input variables in the symbol library is conducted by performing a symbolic operation among input variables with physical units, and transforming the input variables into σ a /E, τ a /G, ε a and γ a after the dimensionless preprocessing.
3 . The method according to claim 1 , wherein the tracking the construction of the expressions by using the array comprises: adopting a binary tree structure by the expression, and using the array to track a suspension situation of tree structure nodes; each time an arithmetic operator node is added, putting a number of child nodes that needs to be suspended in the node into the array; each time the input variables or the constant nodes are added, decreasing the number of the child nodes at the end of the array by one, wherein this process is repeated until the array is empty, indicating that the construction of the expressions is completed; controlling a length of the expressions comprises: constraining the length of the expressions by limiting the number of arithmetic operator nodes; imposing the constraint on a constant operation comprises: constraining the number of the constant nodes, and restricting a constant arithmetic operation; and imposing the constraint on function nesting comprises: constraining a nesting operation of unary functions.
4 - 5 . (canceled)
6 . A device for predicting fatigue life of a turbine blade based on logic constraint-enhanced symbolic regression, comprising a memory and one or more processors, wherein the memory stores executable codes, and when being executed by the one or more processors, the executable codes are used to implement the f method according to claim 1 .
7 . A non-transitory computer-readable storage medium having a program stored thereon, wherein when being executed by a processor, the program is used to implement the method according to claim 1 .

Description

TECHNICAL FIELD The present invention relates to the technical field of fatigue life prediction of aero-engine turbine blades, and in particular relates to a fatigue life prediction method of a turbine blade based on logic constraint-enhanced symbolic regression. BACKGROUND TECHNOLOGY As a key component of an aero-engine, a fatigue life of a turbine blade directly affects safety and reliability of an aircraft. An operating environment of the aero-engine has typical “three high” characteristics, namely a high temperature, a high pressure, and a high speed. There are various forms of blade failures, comprising a fatigue failure, a creep failure, and a high-temperature damage, etc. A fatigue damage caused by alternating loads is one of the most common failure types of blade structures. Due to a complex failure mechanism of a key component and a tiny crack, it is difficult to detect a defect such as a tiny crack on the blade even through a regular inspection. Therefore, an ability to conveniently and accurately predict the fatigue life of the blade has gradually become a focus of attention in both academia and industry. Currently, there are various methods for predicting the fatigue life of the blade. One of the widely used methods is to analyze historical or real-time key parameters measured by sensors on the blade, such as temperature, stress, strain, and vibration. By conducting a time-series prediction of these key parameters and combining with failure cases, time of the blade failure can be predicted. However, due to shortage of failure cases and data, researchers have gradually attempted to precisely capture an internal relationship between mechanical properties of materials (such as a tensile strength, and ductility) and fatigue properties, so as to establish a more reliable fatigue life prediction model. Traditional theoretical methods have derived a series of empirical formulas for establishing the relationship between the mechanical properties and the fatigue life, such as a Coffin-Manson equation, an FS model, a WHS model, etc. Although these empirical formulas have a certain degree of universality among different materials, they rely on a large amount of fatigue test data, are difficult to adapt to complex working conditions, and are difficult to achieve a high-precision life prediction for a specific material. For example, the Chinese Patent with publication number CN118013814A discloses a life prediction method of a high temperature gas-cooled turbine blade, which comprises the following steps: S1: establishing a reduced-order equation between overall design parameters of a gas turbine and a temperature value of a blade and a stress field through a deep learning algorithm; S2: obtaining a measured temperature value of the blade and a measured stress field corresponding to an actual working condition of the gas turbine through sensors; S3: correcting the reduced-order equation in step S1 according to the measured temperature value and the measured stress field obtained in step S2; S4: calculating the temperature value of the blade and the stress field based on the corrected reduced-order equation in step S3, and predicting the remaining life of the high temperature gas-cooled turbine blade. Data-driven machine learning algorithms provide new ideas for the fatigue life prediction. Many studies have shown that powerful and flexible neural networks can accurately capture an influence trend between the mechanical property parameters of materials and the fatigue life, and find model parameters that best match a data set. However, the neural network is essentially a “black box” model, making it difficult to explain a physical meaning of parameters and their internal influence mechanism, and it has 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 fatigue life evaluation and prediction of turbine blades. Combined with load characteristics of each typical position of the turbine blade during a service process, all typical position at different section heights of the turbine blade are regarded as different service tasks; a meta-learning model is utilized to effectively predict damage parameters of each position of the turbine blade under different service time, improve a blade utilization rate, and reduce a use cost; and aiming at a problem that service data of the turbine blade has a typical time-series correlation but a time series is too short, complete time-series samples of each typical position are packaged into a “pseudo sample” to participate in model training by taking an Long Short-Term Memory (LSTM) network as a base model, and while utilizing the meta-learning to solve the small-sample prediction problem, the time-series correlation of the samples is utilized to improve prediction accuracy of the model. In actual engineering, pe