A data-driven-based modeling method for a digital twin model of an engine turbine blade

Abstract

The present application relates to the field of aero-engine design and simulation technology, in particular to a kind of engine turbine blade digital twin modeling method based on data driving;The present application proposes the modeling method of engine turbine blade digital twin based on data driving, a small amount of sampling is combined with the deviation of physical model, and high-dimensional response data is obtained;Through manifold learning dimension reduction, the manifold structure of model parameters to full-field response is constructed;Uncertainty mapping of parameters to manifold characteristics is established by using chaotic polynomial expansion analysis uncertainty;Further, a stochastic moment mapping model is constructed to realize the rapid prediction of multi-physical field performance probability behavior;Quantify the fluctuation characteristics and visualize, establish a non-intrusive digital twin framework, flexibly cope with multi-field coupling problems;Reduce the dependence on physical testing, and provide a solid guarantee for turbine blade multi-condition performance prediction and optimization.

Description

Technical Field

[0001] This invention relates to the field of aero-engine design and simulation technology, specifically a data-driven digital twin modeling method for engine turbine blades. Background Technology

[0002] As a core component of aero-engines, the stability and reliability of turbine blades have a crucial impact on the overall operational efficiency and safety of the engine. Turbine blades endure complex mechanical and thermodynamic loads under extreme operating environments (high temperature, high pressure, high-speed rotation), including thermal stress and mechanical stress generated by gas flow, requiring the blades to maintain extremely high structural integrity and durability. However, due to various uncertainties such as material properties, manufacturing processes, and operating conditions, the actual performance of turbine blades often deviates from design expectations, and this deviation limits the optimization of engine performance.

[0003] Traditional turbine blade design and analysis methods primarily rely on deterministic computational models. These models have limitations in handling complex physical phenomena and multi-source uncertainties, making it difficult to fully capture and quantify performance fluctuations under actual operating conditions. With the rapid development of computer technology and simulation science, digital twin technology, as an emerging modeling and analysis tool, achieves precise mapping and real-time interaction between physical and digital spaces by constructing virtual mirror images of physical objects, providing a new approach for turbine blade performance prediction and optimization design.

[0004] However, existing digital twin technology still faces many challenges when applied to turbine blade modeling: Complexity of application scenarios: The working environment of turbine blades is extreme and variable, involving physical processes that cross multiple disciplines, such as thermodynamics, fluid mechanics, and solid mechanics. This places extremely high demands on the accuracy and robustness of digital twin models.

[0005] The complexity of modeling steps and details: Building an accurate digital twin model of a turbine blade requires detailed modeling steps and precise parameter settings, including the establishment of a thermo-coupled finite element model, the determination of model parameter deviation models, and the collection and processing of sample data. Errors in each step may accumulate and affect the prediction accuracy of the final model.

[0006] Limitations of the stochastic moment mapping (SMR) model: In existing digital twin technologies, probabilistic behavior prediction often relies on large amounts of sample data for training and validation. This not only increases computational costs but may also lead to insufficient generalization ability of the model under conditions of scarce or unevenly distributed data. Furthermore, traditional methods are inefficient in handling the uncertainty quantification of high-dimensional response fields, making it difficult to quickly and accurately predict uncertain behavior in the overall performance response.

[0007] Accuracy issues in full-field performance response prediction: Predicting the full-field performance response of turbine blades requires comprehensive consideration of the interaction of multiple physical fields and quantities. Existing models often suffer from insufficient accuracy when dealing with such complex problems, making it difficult to accurately reflect the probabilistic characteristics of performance fluctuations and variations under actual working conditions. Summary of the Invention

[0008] To address the aforementioned issues, this invention aims to develop a digital twin modeling method that can efficiently handle multi-source uncertainties, requires minimal sample data, and accurately predict the full-field performance response of turbine blades. This method has significant engineering value and economic implications for improving the accuracy and reliability of engine design.

[0009] The technical solution adopted in this invention is: a data-driven digital twin modeling method for engine turbine blades, comprising the following steps: Step 1: Establish a thermo-mechanical coupling finite element model of the turbine blade, and determine the deviation model of the blade structural parameters based on engineering experience or experimental data. The model parameters include elastic modulus, Poisson's ratio, pressure side load, suction side load, coefficient of thermal expansion, thermal conductivity, internal cooling convection coefficient, suction side convection coefficient, internal cooling environment temperature and external blade environment temperature. Step 2: Based on the deviation model and finite element analysis, an optimized sampling strategy is used to obtain the optimal distribution sample points of the model parameters in the [0,1] cumulative probability space, as well as the corresponding full-field performance response data; Step 3: Use machine learning methods to perform manifold dimensionality reduction on the high-dimensional full-field response data, extract low-dimensional features and corresponding manifold functions according to the total empirical variance criterion, and then construct the manifold structure from model parameters to full-field performance response. Step 4: Perform uncertainty propagation analysis on the dimensionality-reduced features using the chaotic polynomial expansion method, solve the coefficients of the chaotic polynomial model to estimate the uncertainty of the low-dimensional manifold features, and establish an uncertainty mapping model between model parameters and manifold features. Step 5: Based on the manifold structure, establish a stochastic moment mapping model between low-dimensional manifold characteristics and the full-field thermodynamic performance response of the blade, so as to realize the rapid prediction of the probabilistic characteristics of the multi-physics field performance of the blade under the multi-source deviation of the model parameters. Step 6: Sample the mean, variance, skewness, and kurtosis to measure the probabilistic characteristics of the full-field response, and visualize the deviation or fluctuation of the blade's physical performance using the maximum entropy principle.

[0010] The deviation model in step 1 uses a probability distribution model to characterize the uncertainty of each model parameter.

[0011] Step 2 first obtains the sample data with the optimal distribution in the cumulative probability space [0,1] according to the following minimization criterion. (8) in For any two points and ascending set of distances The first in j A distance, This means that the distance between all pairs of sample points is exactly equal to The number of point pairs. The optimal sample data in the parameter space can be obtained by the following formula. (9) In the formula For parameter-based x Probability distribution optimization function. Based on the above sampling strategy, the parameters of the model of interest can be obtained. Corresponding sample data Then, finite element simulations were performed to obtain the corresponding full-field performance response data. , . Step 3 is performed according to the following formula. (10) In the formula , By solving equation (3), the corresponding manifold features and eigenvectors can be obtained. The sorted eigenvalues ​​are... The corresponding feature vector is Based on the total empirical variance criterion, according to The number of effective low-dimensional features can be determined. For the retained... Low-dimensional features, whose manifold structure can be represented as (11) Based on the aforementioned manifold structure, high-dimensional data in the original space can be compressed into low-dimensional data in the manifold space, preserving most of the information in the large dataset. Furthermore, this structure can also be used for overlaying. The information contained in the low-dimensional features is used to reconstruct the high-dimensional response.

[0012] Step 4 obtains the first two origin moments of the manifold feature using the following formula. (12) In the formula For the establishment of the first t The coefficients of a chaotic polynomial model with low-dimensional features can be minimized by the following: L 2-norm residuals obtained (13) In the formula, Indicates the firsti A high-dimensional response The low-dimensional characteristic response after manifold compression. For higher-order origin moments. and According to equation (6), the response is used and To construct the corresponding chaotic polynomial and get.

[0013] Step 5 establishes a stochastic moment mapping model between low-dimensional manifold characteristics and overall performance response using the following formula. (14) In the formula These are the coefficients of the quadratic expansion. k =1, 2, 3, 4. Based on this, a stochastic moment mapping model between low-dimensional manifold features and overall performance response was established. The first four raw moments of each high-dimensional response can be obtained through the first four raw moments of the low-dimensional feature response.

[0014] Step 1 involves visualizing the uncertainty characteristics of the full-field response, such as fluctuations and variations, using the following formula. (15) Based on the above random moments, the probability density function of the response can be solved using the maximum entropy principle, thus visualizing its probability distribution characteristics.

[0015] The method further includes an adaptive adjustment step for the complexity of the application scenario. By monitoring the changes in the working environment parameters of the turbine blade in real time, the boundary conditions and material property parameters in the thermo-coupling finite element model are dynamically adjusted to achieve accurate simulation of the uncertain energy of the turbine blade under different working conditions.

[0016] The method introduces automated process control in the modeling steps, automatically executing steps 1 to 6 through preset scripts or software tools, reducing human intervention, improving modeling efficiency and consistency, and ensuring the accuracy and repeatability of modeling details.

[0017] The stochastic moment mapping model, by introducing high-order chaotic polynomial expansion and reinforcement learning algorithms, iteratively optimizes the mapping relationship between low-dimensional manifold features and overall performance response, thereby improving the accuracy and generalization ability of the stochastic moment mapping model and achieving high-precision simulation and prediction of the probabilistic behavior of overall performance response.

[0018] The beneficial effects of this invention are as follows: This invention innovatively proposes a digital twin model construction technology for engine turbine blades. This technology can systematically quantify the global effects of key environmental, structural, and material factors on blade performance, achieving comprehensive prediction, in-depth analysis, and precise understanding of blade mechanical behavior under arbitrary inputs and their deviation fluctuations. Simultaneously, this invention constructs a data-driven, non-intrusive digital twin model framework. This framework requires only limited sample data and does not require altering the existing structural system to efficiently predict the uncertainty fluctuations and variation characteristics of structural behavior, providing a flexible and powerful solution for structural performance evaluation and optimization design under complex multi-field coupling environments. The invention provides a powerful modeling and analysis tool. Furthermore, the digital twin model construction strategy employed in this invention cleverly integrates manifold learning and multinomial chaotic expansion techniques, successfully transforming the challenge of quantifying the uncertainty of high-dimensional structural response fields into efficient analysis in low-dimensional feature spaces. It constructs an accurate mapping model from model parameters to the random moments of the high-dimensional response field, intuitively presenting the probability distribution characteristics of mechanical behavior at any position. This significantly improves the efficiency and accuracy of model construction and demonstrates significant beneficial effects in multiple aspects. It not only enhances the accuracy of predicting the probabilistic characteristics of turbine blade performance but also optimizes the modeling process and reduces computational costs. Specifically, this is reflected in the following aspects: (1) Comprehensive assessment of the global impact of key factors on blade performance: This invention, by constructing a digital twin model of engine turbine blades, can systematically consider the comprehensive impact of various key factors such as environment, structure, and materials on blade performance. Compared with traditional methods, this invention is no longer limited to the analysis of a single or a few parameters, but comprehensively integrates these complex factors, realizing a global quantitative assessment of blade structural performance. This characteristic makes this invention more accurate and comprehensive in predicting, analyzing, and understanding the mechanical behavior of blades under different input conditions and their deviation fluctuations, providing a more scientific basis for the optimized design of turbine blades.

[0019] (2) Effectively addressing the complexity of application scenarios: Given the extreme and variable working environment of turbine blades and the complexity of multidisciplinary physical processes, this invention constructs a comprehensive digital twin model, integrating knowledge from thermodynamics, fluid mechanics, solid mechanics, and other disciplines, to achieve accurate simulation of complex physical phenomena. This method not only considers the thermal and mechanical stresses of the blades under high temperature, high pressure, and high-speed rotation, but also comprehensively considers various uncertainties such as material properties, manufacturing processes, and operating conditions, thus more accurately reflecting the performance of the blades under actual working conditions. This comprehensive simulation capability provides strong support for the performance evaluation and optimization design of turbine blades in complex application scenarios.

[0020] (3) Simplifying modeling steps and details, and improving modeling efficiency: The construction process of traditional turbine blade digital twin models is cumbersome and complex, involving a large number of modeling steps and fine parameter settings. This invention significantly simplifies the modeling process and reduces the requirements for modeling details by introducing advanced algorithms such as optimized sampling strategies, machine learning methods, manifold learning, and polynomial chaotic expansion. Specifically, optimized sampling strategies can obtain the most representative initial sample points with limited sample data, reducing the number of simulations; machine learning methods can automatically extract key features from high-dimensional data, reducing the complexity of data processing; and manifold learning and polynomial chaotic expansion effectively reduce the difficulty of quantifying high-dimensional uncertainty problems and improve modeling efficiency. These improvements make the modeling method of this invention more efficient and convenient, and reduce the requirements for the professional skills of modelers.

[0021] (4) Overcoming the limitations of uncertainty behavior prediction: The acquisition of uncertain characteristics in existing digital twin technologies often relies on a large amount of sample data for training and verification, resulting in high computational costs and insufficient generalization ability. This invention transforms the uncertainty quantification problem of high-dimensional structural response fields into uncertainty analysis of low-dimensional features by combining manifold learning and polynomial chaotic expansion methods, thereby significantly reducing the requirement for sample data. At the same time, this method estimates the uncertainty of low-dimensional manifold features by solving the coefficients of the chaotic polynomial model, and then establishes an uncertainty mapping model between model parameters and manifold features. This mapping model not only has high accuracy and robustness, but also can quickly and accurately achieve probabilistic behavior prediction of the entire field performance, overcoming the limitations of existing technologies.

[0022] (5) Improving the accuracy of probabilistic simulation of full-field performance: Probabilistic simulation and prediction of the full-field performance response of turbine blades requires comprehensive consideration of the interaction of multiple physical fields and quantities. Existing models often suffer from insufficient accuracy when dealing with such complex problems. This invention achieves rapid simulation and prediction of the uncertain response of the full field by constructing a stochastic moment mapping model between low-dimensional manifold characteristics and the thermodynamic full-field performance response of the blade. This model quantifies the fluctuation and variation characteristics of the full-field response by sampling statistics such as mean, variance, skewness, and kurtosis, and visualizes the uncertainty state of the blade's physical performance through the maximum entropy principle. This prediction method not only improves the accuracy and reliability of the prediction, but also enables designers to intuitively understand the performance of the blade under different operating conditions and its uncertainty range, providing a more scientific basis for optimization design. Attached Figure Description

[0023] Figure 1 This is the blade structure model in this invention; Figure 2 This is a schematic diagram comparing the prediction accuracy of low-dimensional manifold features in this invention; Figure 3 This is a schematic diagram of the random moment distribution field of the digital twin model in this invention; Figure 4 This is a visual schematic diagram of the probability distribution characteristics of the digital twin model in this invention. Detailed Implementation

[0024] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and, together with the invention, serve to illustrate the principles of the invention.

[0025] like Figure 1-4 As shown, the method of the present invention can be adapted for the construction of digital twin models of engine turbine blades, and can also be applied to other arbitrary structural models. To illustrate the technical solution of the present invention in more detail, a turbine blade is used as an example. Specifically, a data-driven digital twin modeling method for engine turbine blades includes the following steps: Step 1: Establish a thermo-mechanical coupling finite element model of the turbine blade, and determine the deviation model of the blade structural parameters based on engineering experience or experimental data. The model parameters include elastic modulus, Poisson's ratio, pressure side load, suction side load, coefficient of thermal expansion, thermal conductivity, internal cooling convection coefficient, suction side convection coefficient, internal cooling environment temperature, and external blade environment temperature.

[0026] This invention provides a structural model of an engine turbine blade, such as... Figure 1 The blade shown has an internal cooling duct that uses cold air to maintain its temperature within the material's limits, while high-pressure gas applies pressure to both the suction and pressure sides. The corresponding finite element model of the blade structure includes 11,794 elements and 21,252 nodes, with a high-dimensional response of 21,252 dimensions. Furthermore, 12 arbitrary locations are shown in the figure to visualize the probabilistic response characteristics. The model parameters of the digital twin model constructed in this embodiment mainly include key parameters related to the environment, structure, and materials that need to be considered in blade design, such as elastic modulus, Poisson's ratio, pressure-side load, suction-side load, coefficient of thermal expansion, thermal conductivity, internal cooling convection coefficient, suction-side convection coefficient, internal cooling environment temperature, and external blade environment temperature. Deviation values ​​and corresponding distribution models of the 10-dimensional model parameters are also provided.

[0027] Step 2: Based on the deviation model and finite element analysis, an optimized sampling strategy is used to obtain the optimal distribution sample points of the model parameters in the [0,1] cumulative probability space, as well as the corresponding full-field performance response data.

[0028] In this invention, 100 samples are extracted based on the distribution characteristics of a 10-dimensional variable. First, the optimal distribution of sample data in the [0,1] cumulative probability space is obtained according to the following minimization criterion. (16) in Let distances between any two points be the ascending set. The first in j A distance, This means that the distance between all pairs of points is exactly equal to The number of point pairs. The optimal sample data in the parameter space can be obtained by the following formula. (17) In the formula For parameter-based x The optimization function of the probability distribution model. Based on the above sampling strategy, sample data corresponding to the model parameters of interest can be obtained. Then, finite element simulations were performed to obtain the corresponding full-field performance response data. , .

[0029] Step 3: Use machine learning methods to perform manifold dimensionality reduction on the high-dimensional full-field response data, extract low-dimensional features and corresponding manifold functions according to the total empirical variance criterion, and then construct the manifold structure from model parameters to full-field performance response.

[0030] In this invention, based on response data Solve for the corresponding mean vector Covariance Matrix Subsequently, the corresponding manifold characteristic parameters and eigenvectors can be obtained by solving the following equation. (18) The feature values ​​sorted by size are The feature vector is Based on the total empirical variance criterion Six main low-dimensional features and their corresponding eigenvectors can be identified, and their manifold structure can be represented as follows: (19) Based on the above manifold structure, the 21252-dimensional data in the original space can be compressed into 6-dimensional data in the manifold space. (6-dimensional manifold features) With feature vectors It retains 99% of the information in the original dataset.

[0031] Step 4: Perform uncertainty propagation analysis on the dimensionality-reduced features using the chaotic polynomial expansion method, solve the coefficients of the chaotic polynomial model to estimate the uncertainty of the low-dimensional manifold features, and establish an uncertainty mapping model between model parameters and manifold features. In this invention, an uncertainty mapping model between 10-dimensional model parameters and 6-dimensional manifold features is constructed using the chaotic polynomial expansion method. First, a chaotic polynomial model is constructed between the model parameters and each feature. The core of this model is to determine the coefficients of the chaotic polynomial model based on the variables and response data using the following formula. (20) In the formula, Indicates the first i A high-dimensional response The low-dimensional characteristic response after manifold compression. Due to the orthogonality of chaotic polynomials, their origin moments can be directly obtained from the coefficients of the chaotic polynomial model. (twenty one) The above process can only obtain the first and second order raw moments. For the third and fourth order raw moments... and The square and cubic values ​​of the response can be used. and The corresponding chaotic polynomial model is constructed using the same process. and To verify the effectiveness of the constructed chaotic polynomial model of manifold features, the Monte Carlo method was used to extract 10,000 samples from the 10-dimensional variables, and the corresponding manifold features were then solved. This was then compared mechanically with the model features calculated by the chaotic polynomial model. For example... Figure 2 The comparison results show that the constructed chaotic polynomial model has good prediction accuracy for the fluid characteristics of the full-field stress response of this blade.

[0032] Step 5: Based on the manifold structure, establish a stochastic moment mapping model between low-dimensional manifold characteristics and the full-field thermodynamic performance response of the blade, thereby constructing a digital twin model of the engine turbine blade and realizing rapid prediction of the probabilistic characteristics of the fluctuation and variation of the full-field physical performance of the blade under multi-source deviations of model parameters.

[0033] In this invention, the origin moments of the high-dimensional full-field response are obtained based on the origin moments of the low-dimensional manifold features, and a digital twin model is established to achieve probabilistic prediction of multi-field responses under multiple physical quantities. According to the following formula, the fourth-order origin moments of the 21252-dimensional full-field response can be analytically obtained from the first four order origin moments of the 6-dimensional low-dimensional features. (twenty two) In the formula These are the coefficients of the quadratic expansion. k =1, 2, 3, 4. Based on this, a digital twin model of the engine turbine blades was established, which can realize the probabilistic behavior simulation of the full-field response from 10-dimensional model parameters to 21252-dimensional parameters.

[0034] Step 6: Sample the mean, variance, skewness, and kurtosis to quantify the fluctuation and variation characteristics of the overall response, and visually characterize the uncertainty of the blade's physical properties.

[0035] In this invention, the original moments of the response are transformed into corresponding random moments such as mean, standard deviation, skewness, and kurtosis using the following formula, thereby enabling visualization of the probabilistic behavior of the response field.

[0036] (twenty three) Figure 3 The mean and standard deviation fields of the blade response are presented. Based on the aforementioned random moments, the probability density function of the response can be solved using the maximum entropy principle, thus visualizing its uncertain distribution characteristics. To verify the effectiveness of the constructed digital twin model, the random moments of the response field were calculated using 10,000 samples obtained through the aforementioned Monte Carlo method. Furthermore, the random moments at 12 nodes are given. It can be observed that the digital twin model constructed in this patent accurately predicts the mean and standard deviation at all 12 locations, but errors exist in the skewness and kurtosis at some locations. A significant factor contributing to this phenomenon is that some values ​​from the Monte Carlo method are relatively close to 0, such as the skewness at position 9, resulting in a relatively large error. Figure 4 The probability distribution characteristics of the stress response at each node are visualized in the image. Figure 3 , Figure 4 The comparison results show that the results of the digital twin model and the Monte Carlo method are in strong agreement, thus demonstrating the effectiveness of constructing the digital twin model for probabilistic behavior simulation.

[0037] This invention establishes a non-intrusive modeling framework by combining manifold learning and multinomial chaotic expansion. By constructing a digital twin model of the model parameters and the full-field structural response of the blade, it achieves simulation of multiple physical quantities, multiple physical fields, and multiple probabilities of the structure. Furthermore, this method is based on only limited sample data and requires no modification to the existing structural system, thus significantly reducing the computational cost of analyzing the complex mechanical behavior of structures. It provides an effective approach for the rapid and accurate prediction of the probabilistic mechanical behavior of blade structures under arbitrary inputs and their deviation fluctuations, and also lays an important theoretical foundation for the refined design of turbine blades.

[0038] Example 1: A Data-Driven Digital Twin Modeling Method for Engine Turbine Blades This embodiment focuses on a turbine blade of a certain type of aero-engine, employing a data-driven approach to construct its digital twin model, aiming to improve the accuracy and reliability of blade performance prediction. Turbine blades face complex mechanical and thermodynamic challenges under high temperature, high pressure, and high-speed rotational environments, thus requiring a modeling method that comprehensively considers the interactions of multiple physical fields and quantities.

[0039] Step 1: Establish a thermo-mechanical coupled finite element model of the turbine blades First, based on the geometric dimensions and material properties of the turbine blades, a three-dimensional thermo-mechanical coupling model was established in finite element analysis software. The model considered key parameters such as the blade's elastic modulus, Poisson's ratio, and coefficient of thermal expansion, and set corresponding boundary conditions, such as pressure-side load, suction-side load, and internal cooling environment temperature.

[0040] Step 2: Determine the blade model parameter deviation model Based on engineering experience or experimental data, deviation models are established for key parameters in the model. For example, the elastic modulus and coefficient of thermal expansion may fluctuate within a certain range due to batch differences in materials. These fluctuation ranges can be characterized by probability distribution models (such as normal distribution, log-normal distribution, etc.).

[0041] Step 3: Optimize sampling strategy to obtain sample data An optimized sampling strategy (such as Latin hypercube sampling or maximizing minimum distance sampling) is employed to generate a set of representative initial sample points in the parameter space. Then, finite element analysis software is used to simulate these sample points and obtain the corresponding full-field performance response data, including temperature and stress fields.

[0042] Step 4: Machine learning methods for manifold dimensionality reduction The collected high-dimensional full-field response data is input into machine learning algorithms (such as Principal Component Analysis (PCA), Locally Linear Embedding (LLE), etc.) for manifold dimensionality reduction. Low-dimensional features and their corresponding manifold functions are extracted based on the total empirical variance criterion, and the manifold structure from model parameters to full-field performance response is established.

[0043] Step 5: Perform uncertainty propagation analysis using chaotic polynomial expansion. Uncertainty propagation analysis is performed on the dimensionality-reduced features using chaotic polynomial expansion methods (such as generalized polynomial chaos GPC, sparse polynomial chaos SPC, etc.). By solving the coefficients of the chaotic polynomial model, the uncertainty of the low-dimensional manifold features is estimated, and an uncertainty mapping model between model parameters and manifold features is established.

[0044] Step 6: Establish a stochastic moment mapping model to construct a digital twin model Based on manifold structure, a stochastic moment mapping model is established to map low-dimensional manifold characteristics to the full-field thermodynamic performance response of the blade. This model enables rapid prediction of the fluctuations and variations in the full-field physical properties of the blade under multi-source deviations in model parameters.

[0045] Step 7: Quantify and visualize the uncertainty of the overall response. The fluctuation and variability of the overall response are quantified using statistical measures such as sampling mean, variance, skewness, and kurtosis. The probability density function of the response is solved using the maximum entropy principle, and the uncertainty of the blade's physical properties is visualized through graphs, contour plots, and other methods.

[0046] This embodiment successfully constructed a digital twin model of a turbine blade for a certain type of aero-engine, enabling performance prediction of the blade under complex operating environments. By optimizing the sampling strategy and applying machine learning methods, the computational and time costs in the modeling process were significantly reduced. Simultaneously, the establishment of the stochastic moment mapping model improved the accuracy and reliability of the overall performance response prediction, providing a scientific basis for the optimized design of the blade.

[0047] Example 2: An application case of a data-driven digital twin modeling method for engine turbine blades This embodiment applies a data-driven digital twin modeling method for engine turbine blades to practical engineering, aiming to improve the overall performance and reliability of the engine.

[0048] Steps 1 to 3: Model building and sample data collection Following steps 1 to 3 in Example 1, a thermo-mechanical coupled finite element model of the turbine blade is established, and the deviation model of the model parameters is determined. Then, an optimized sampling strategy is used to generate initial sample points in the parameter space, and finite element simulation is performed to obtain full-field performance response data.

[0049] Steps 4 to 6: Data Processing and Model Building In step 4, the Locally Linear Embedding (LLE) algorithm is used to perform manifold dimensionality reduction on the high-dimensional full-field response data, extracting key low-dimensional features and their manifold functions. In step 5, the Generalized Multinomial Chaos (GPC) method is used to perform uncertainty propagation analysis on the dimensionality-reduced features, establishing an uncertainty mapping model between model parameters and manifold features. Finally, in step 6, based on the manifold structure and the uncertainty mapping model, a stochastic moment mapping model between the low-dimensional manifold features and the blade thermodynamic full-field performance response is constructed, forming a complete digital twin model.

[0050] Step 7: Performance Prediction and Optimization Design Using a constructed digital twin model, the performance of turbine blades under different operating conditions is predicted. By adjusting model parameters (such as pressure-side load and suction-side load), the changing trend of the blade's overall performance response is observed, and the impact of different design schemes on blade performance is evaluated. Based on the prediction results, the blade design is optimized to improve its performance and reliability in actual operation.

[0051] This embodiment successfully achieved accurate prediction and optimized design of turbine blade performance for a certain aero-engine by applying a data-driven digital twin modeling method for engine turbine blades. The digital twin model not only improved the accuracy and reliability of performance prediction but also provided a scientific basis and intuitive visualization for optimized design. The implementation of the optimized design effectively improved the overall performance and reliability of the engine, reduced R&D costs and time, and has significant engineering value and economic significance.

Claims

1. A data-driven method for modeling digital twin models of engine turbine blades, characterized in that: Includes the following steps: Step 1: Establish a thermo-mechanical coupling finite element model of the turbine blade, and determine the deviation model of the blade structural parameters based on engineering experience or experimental data. The model parameters include elastic modulus, Poisson's ratio, pressure side load, suction side load, coefficient of thermal expansion, thermal conductivity, internal cooling convection coefficient, suction side convection coefficient, internal cooling environment temperature and external blade environment temperature. Step 2: Based on the deviation model and finite element analysis, an optimized sampling strategy is used to obtain the optimal distribution sample points of the model parameters in the [0,1] cumulative probability space, as well as the corresponding full-field performance response data; Step 3: Use machine learning methods to perform manifold dimensionality reduction on the high-dimensional full-field response data, extract low-dimensional features and corresponding manifold functions according to the total empirical variance criterion, and then construct the manifold structure from model parameters to full-field performance response. Step 4: Perform uncertainty propagation analysis on the dimensionality-reduced features using the chaotic polynomial expansion method, solve the coefficients of the chaotic polynomial model to estimate the uncertainty of the low-dimensional manifold features, and establish an uncertainty mapping model between model parameters and manifold features. Step 5: Based on the manifold structure, establish a stochastic moment mapping model between low-dimensional manifold characteristics and the full-field thermodynamic performance response of the blade, so as to realize the rapid prediction of the probabilistic characteristics of the multi-physics field performance of the blade under the multi-source deviation of the model parameters. Step 6: Sample the mean, variance, skewness, and kurtosis to measure the probabilistic characteristics of the full-field response, and visualize the deviation or fluctuation of the blade's physical performance using the maximum entropy principle.

2. The data-driven digital twin modeling method for engine turbine blades according to claim 1, characterized in that: The deviation model in step 1 uses a probability distribution model to characterize the uncertainty of each model parameter.

3. The data-driven digital twin modeling method for engine turbine blades according to claim 1, characterized in that: Step 2 first obtains the sample data with the optimal distribution in the cumulative probability space [0,1] according to the following minimization criterion. （1） in For any two points and ascending set of distances The first in j A distance, This means that the distance between all pairs of sample points is exactly equal to The number of point pairs; the optimal sample data in the parameter space can be obtained by the following formula. （2） In the formula For parameter-based x The probability distribution optimization function can be used to obtain the model parameters of interest based on the above sampling strategy. Corresponding sample data Then, finite element simulations were performed to obtain the corresponding full-field performance response data. , .

4. The data-driven digital twin modeling method for engine turbine blades according to claim 1, characterized in that: Step 3 is performed according to the following formula. (3) In the formula , By solving equation (3), the corresponding manifold features and eigenvectors can be obtained. The sorted feature values ​​are The corresponding feature vector is ; Based on the total empirical variance criterion, according to The number of effective low-dimensional features can be determined; for the preserved Low-dimensional features, whose manifold structure can be represented as （4） Based on the aforementioned manifold structure, high-dimensional data in the original space can be compressed into low-dimensional data in the manifold space, preserving most of the information in the large dataset; simultaneously, this structure can also be used for overlay. The information contained in the low-dimensional features is used to reconstruct the high-dimensional response.

5. The data-driven digital twin modeling method for engine turbine blades according to claim 1, characterized in that: Step 4 obtains the first two origin moments of the manifold feature using the following formula. （5） In the formula For the establishment of the first t The coefficients of a chaotic polynomial model with low-dimensional features can be minimized by the following: L 2-norm residuals obtained （6） In the formula, Indicates the first i A high-dimensional response Low-dimensional characteristic response after manifold compression; for higher-order origin moments and According to equation (6), the response is used and To construct the corresponding chaotic polynomial and get.

6. The data-driven digital twin modeling method for engine turbine blades according to claim 1, characterized in that: Step 5 establishes a stochastic moment mapping model between low-dimensional manifold characteristics and overall performance response using the following formula. （7） In the formula These are the coefficients of the quadratic expansion. k =1, 2, 3, 4; Based on this, a stochastic moment mapping model of low-dimensional manifold features and overall performance response was established. The first four original moments of each high-dimensional response can be obtained through the first four original moments of the low-dimensional feature response.

7. The data-driven digital twin modeling method for engine turbine blades according to claim 1, characterized in that: Step 1 involves visualizing the uncertainty, fluctuation, and variability characteristics of the full-field response using the following formula. Based on the above random moments, the probability density function of the response can be solved using the maximum entropy principle, thus visualizing its probability distribution characteristics.

8. A data-driven digital twin modeling method for engine turbine blades according to any one of claims 1-7, characterized in that: The method further includes an adaptive adjustment step for the complexity of the application scenario. By monitoring the changes in the working environment parameters of the turbine blade in real time, the boundary conditions and material property parameters in the thermo-mechanical coupled finite element model are dynamically adjusted to achieve accurate simulation of the probabilistic performance of the turbine blade under different working conditions.

9. A data-driven digital twin modeling method for engine turbine blades according to any one of claims 1-7, characterized in that: This method introduces automated process control into the modeling steps, automatically executing steps 1 to 6 through preset scripts or software tools, reducing human intervention, improving modeling efficiency and consistency, and ensuring the accuracy and repeatability of modeling details.

10. The data-driven digital twin modeling method for engine turbine blades according to claim 6, characterized in that: The stochastic moment mapping model, by introducing high-order chaotic polynomial expansion and reinforcement learning algorithms, iteratively optimizes the mapping relationship between low-dimensional manifold features and overall performance response, thereby improving the accuracy and generalization ability of the stochastic moment mapping model and achieving high-precision simulation and prediction of the probabilistic behavior of overall performance response.

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