A Method for Constructing Reduced-Order Models of Temperature and Stress Fields in Turbine Blades

Abstract

This invention proposes a method for constructing reduced-order models of the temperature and stress fields of turbine blades, comprising: obtaining the change history of boundary condition parameters required for fluid-structure interaction (FSI) and static simulation of turbine blades during service; training a Wasserstein variational autoencoder using a momentum-based stochastic gradient descent optimization algorithm; establishing FSI and static simulation models of the turbine blades; constructing reduced-order flow field models for temperature and stress field sample sets using intrinsic orthogonal decomposition theory, and obtaining the solution space basis functions of the reduced-order flow field models; establishing a surrogate model using the radial basis function method; during service, using the actually changing parameters as input to the surrogate model to obtain the reduced-order basis function coefficients, and linearly superimposing the basis functions through intrinsic orthogonal decomposition to obtain the reduced-order temperature and stress field models of the turbine blades. According to the technical solution of this invention, the offline construction cost of the reduced-order model is reduced.

Description

Technical Field

[0001] This invention belongs to the field of aero-engines, and specifically relates to a method for constructing a reduced-order model of the temperature field and stress field of turbine blades. Background Technology

[0002] Condition monitoring and predictive maintenance of aero-engines are crucial methods for ensuring the structural safety of aero-engines, extending aircraft lifespan, fully realizing the lifespan potential of aero-engines, and guaranteeing combat capabilities. With the development of aero-engine health monitoring technology and the rise of the digital twin concept, single-engine life management concepts and technologies based on actual usage have emerged. These technologies achieve health monitoring and lifespan management during the aero-engine's operation by constructing a high-fidelity digital model of the aero-engine and integrating on-site monitoring data.

[0003] However, traditional high-fidelity digital models often employ numerical methods such as the finite element method and the finite volume method, which are frequently computationally intensive and difficult to meet the real-time requirements of lifespan monitoring. In recent years, reduced-order modeling techniques have been proposed to replace traditional simulation models for rapid calculation of online processes. Current reduced-order modeling techniques involve independently and uniformly sampling the variation range of each parameter in the model to construct a sample set for reduced-order modeling. However, this approach faces the dimensionality explosion problem when dealing with high-dimensional variables and can lead to samples that do not accurately represent the actual flight process, increasing the complexity of the reduced-order model.

[0004] Existing patent CN116842641A, "A Method for Reconstructing the Global Physical Field of Turbine Blades Based on Intrinsic Orthogonal Decomposition," discloses a method for reconstructing the global physical field of turbine blades. This method calculates a set of reduced-order orthogonal vectors from a snapshot matrix, which serve as the main modes of the physical field distribution. The global physical field of the turbine blade is then reconstructed based on a finite number of sensor measurements and the main modes. However, existing research indicates that the selection of sample points significantly impacts the reduction-order orthogonal vectors. Traditional sampling methods for reducing the order of temperature and stress fields in turbine blades suffer from problems such as unreasonable sample selection and low construction efficiency.

[0005] Existing patent CN115455819A, "An Intelligent Modeling Method for Transient Flow Field Migration and Order Reduction under Multiple Operating Conditions in Turbine Blades," discloses an intelligent modeling method for transient flow field migration and order reduction under multiple operating conditions. This method obtains data from several monitoring points on a preset cross-section by performing transient calculations on preset operating conditions, and then constructs a reduced-order model based on this data. However, in actual turbine blade operation, the operating conditions are in a dynamic process, and this method lacks consideration for changes in boundary conditions, as well as the order reduction process for the temperature and stress fields of the turbine blade solid.

[0006] Therefore, it is necessary to develop a sample set sampling method for a reduced-order model applicable to the service process of aero-engine turbine blades, so as to solve the problems of high construction cost and difficulty in application of the reduced-order model of turbine blade temperature field / stress field in the offline stage. Summary of the Invention

[0007] Therefore, the present invention provides a method for constructing a reduced-order model of the temperature field and stress field of turbine blades, in an attempt to solve or at least alleviate the problems mentioned above.

[0008] The method includes:

[0009] Step S110: Obtain the change history of boundary condition parameters required for fluid-structure heat transfer simulation and static simulation of turbine blades during service. The boundary condition parameters include the total temperature and total pressure at the turbine main flow inlet, the total temperature and total pressure at the cooling airflow inlet, the static pressure at the turbine main flow outlet, and the rotational speed.

[0010] S120. After obtaining the change history of boundary condition parameters, the group is divided according to the range of rotation speed change. Several points are extracted from each group. 70% of them are selected to form the Wasserstein Auto-Encoder (WAE) training set, and 30% are selected to form the Wasserstein Auto-Encoder validation set. The Wasserstein Auto-Encoder is trained using the momentum-based stochastic gradient descent optimization algorithm.

[0011] S130, establish a fluid-structure heat transfer simulation model and a static simulation model of the turbine blade;

[0012] S140, Distribution of Low-Dimensional Latent Variables Latin hypercube sampling is performed. Based on the Wasserstein variational autoencoder established in step S120, the parameters of the sample calculation points are generated as inputs to the turbine blade fluid-structure heat transfer simulation model and turbine blade static simulation model in step S130. The turbine blade temperature field and stress field sample sets are obtained. The flow field reduced-order model of the temperature field sample set and stress field sample set is constructed using the intrinsic orthogonal decomposition theory. The solution space basis functions of the flow field reduced-order model are obtained.

[0013] S150, combining the solution space basis functions determined in step S140, obtain the boundary condition parameters - turbine blade temperature field dataset. Boundary condition parameters - turbine blade stress field dataset The coefficients of each solution expressed in terms of basis functions Construct a dataset of boundary condition parameters - turbine blade temperature field basis function coefficients. Boundary condition parameters - Turbine blade stress field basis function coefficients dataset The radial basis function method is used to establish... and The proxy model is defined as follows: f is the mapping relationship between boundary condition parameters and turbine blade temperature field basis function coefficients, and g is the mapping relationship between boundary condition parameters and turbine blade stress field basis function coefficients.

[0014] During service, the S160 uses the actual changing parameters as input to the surrogate model to obtain the reduced-order basis function coefficients. The basis functions are then linearly superimposed through intrinsic orthogonal decomposition to obtain the reduced-order model of the turbine blade temperature field and stress field.

[0015] In the above method, the parameters that actually change include the total temperature and pressure at the turbine mains inlet, the total temperature and pressure at the cooling air inlet, the static pressure at the turbine mains outlet, and the rotational speed.

[0016] In the above method, the loss function of the Wasserstein variational autoencoder consists of two parts: reconstruction loss and regularization factor. The reconstruction loss uses the mean squared error loss, and its expression is as follows: , where x is the service parameter. Here, n is the number of encoder outputs, and the regularization uses the maximum average difference, expressed as:

[0017] ,

[0018] In the formula, Q is the latent variable distribution of the actual output of the encoder, D is the divergence between the latent variable target distribution and the actual distribution, λ is the hyperparameter, X is the training parameter, G is the decoder output, and c(X,G(Z)) represents the distance metric between the training parameter and the decoder output.

[0019] In the above method, the fluid-structure heat transfer simulation model includes turbine flow channel and turbine blade model, and the boundary conditions include the total temperature and pressure at the inlet of the main flow and blade cooling channel and the static pressure at the outlet of the turbine flow channel. The static simulation model includes turbine blade model, and the loads are the temperature field heat, stress and rotational speed calculated by the heat transfer model.

[0020] The beneficial effects of the technical solution of this invention are:

[0021] 1. This invention employs the Wasserstein distance from the Optimal Transport (OT) method, matching PZ with a continuous mixture distribution QZ of latent variables. This ensures that the latent codes of different samples may be far apart, improving the encoder reconstruction accuracy. It effectively solves the posterior collapse problem of traditional Variational Autoencoders (VAE)-type deep learning generative models, while also exhibiting more stable training compared to them.

[0022] 2. This invention generates the sample set required for the reduced-order model based on the WAE sampler, making the solution space spanned by the sample set more consistent with actual usage, improving the extraction of effective samples, reducing unnecessary basis, and lowering the offline construction cost of the reduced-order model; it has broad application prospects in aero-engine life management and can provide certain technical support for relevant workers. Attached Figure Description

[0023] Figure 1 This is a schematic flowchart illustrating the method for constructing a reduced-order model of the temperature and stress fields of a turbine blade according to an embodiment of the present invention.

[0024] Figure 2 This is a schematic diagram of a historical flight section performance parameter dataset according to an embodiment of the present invention;

[0025] Figure 3 The present invention relates to the structure and training process of a WAE sampler according to an embodiment of the present invention. Detailed Implementation

[0026] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0027] According to the technical solution of this invention, the construction process is divided into offline and online stages. In the offline stage, the inlet and outlet parameters of the flow channel and the rotational speed spectrum required for the turbine blade heat transfer / static simulation during service are first acquired. Then, the turbine blades are divided into groups according to the range of rotational speed variation, and several points are extracted from each group as a Wasserstein Auto-Encoder (WAE) sampler dataset. A momentum-based stochastic gradient descent optimization algorithm is used to train the WAE sampler. Latin hypercube sampling is performed on the low-dimensional latent variable distribution to generate training sample parameters, which are then input into the simulation model to obtain the turbine blade temperature and stress field sample sets. Finally, a reduced-order flow field model is constructed using Proper Orthogonal Decomposition (POD) theory. Singular value decomposition is used to obtain the solution space basis and the coefficients of each solution represented by basis functions. A radial basis function interpolation method is used to establish a surrogate model for the temperature and stress fields using POD coefficients. During online service, the actual monitored changing parameters are used as input to the surrogate model to obtain the reduced-order basis coefficients. The turbine blade temperature and stress fields are quickly obtained by linearly superimposing the basis functions POD. To ensure that the generated parameters cover as many possible parameters as possible during the service process, the number of parameter points is increased for speed ranges with more maneuvers.

[0028] Figure 1 This is a schematic flowchart illustrating a method for constructing a reduced-order model of the temperature and stress fields of a turbine blade according to an embodiment of the present invention. (Refer to the following...) Figure 1 Describe the process of constructing this order reduction model. For example... Figure 1 As shown, the method includes the following steps:

[0029] Step S110: Obtain the boundary condition parameter variation history required for the fluid-structure heat transfer simulation and static simulation of the turbine blades during service. The boundary condition parameters include the total temperature and pressure at the turbine mains inlet, the total temperature and pressure at the cooling airflow inlet, the static pressure at the turbine mains outlet, and the rotational speed. These boundary condition parameters are obtained from flight parameters recorded by the flight recorder during actual flight, combined with the engine's overall performance calculation model. The boundary condition parameter variation history during service should be no less than 10 sets. For example, the boundary condition parameter variation history for the fluid conjugate heat transfer and structural static simulation of the turbine blades during service is as follows: Figure 2 As shown.

[0030] S120: After obtaining the boundary condition parameter history, the system is divided into groups based on the rotational speed variation range. Several points are extracted from each group, and 70% of these points form the Wasserstein variational autoencoder training set, while 30% form the Wasserstein variational autoencoder validation set. The Wasserstein variational autoencoder is trained using a momentum-based stochastic gradient descent optimization algorithm. (The latent variable distribution of the Wasserstein variational autoencoder is then described.) The distribution follows a normal Gaussian distribution. The Wasserstein variational autoencoder loss function consists of two parts: reconstruction loss and regularization, where the reconstruction loss uses the mean squared error loss, and its expression is: , where x is the service parameter. For the output of the autoencoder model, n is the number of samples in the training set, and the regularization uses the maximum mean difference, expressed as:

[0031] ,

[0032] In the formula, Z|X is the probability distribution of the boundary condition parameters actually generated by the autoencoder model, Z|X is the conditional probability (the probability of Z given X), and Q is the distribution of the latent variables in the actual output of the encoder. Here, λ represents the probability distribution of the latent variables, i.e., the low-dimensional latent variable distribution. D is the divergence between the target and actual latent variable distributions. λ is a hyperparameter, X is the training parameters, G is the decoder output, c(X, G(Z)) represents the distance metric between the training parameters and the decoder output, and inf denotes the lower bound. Parameters below inf represent arbitrary parameters. The encoder is defined by the subscript X, which represents the training boundary condition parameters, and the subscript Z, which represents the latent variables of the boundary condition parameters after dimensionality reduction.

[0033] For example, each 20% increase in engine speed forms a group, and the corresponding parameter points within the group are selected. Since the 0-20% and 80-100% engine speed ranges correspond to engine operating conditions that only include takeoff and high-speed cruise, while the 20-80% engine speed range may include complex maneuvers, 300 points are extracted from each group for the 20-80% engine speed range, and 150 points are extracted from each of the other ranges to form the WAE sampler training sample. The structure of the WAE sampler is as follows. Figure 3 As shown, its latent variable distribution is normal, and its variance is 2.

[0034] S130, establish a turbine blade fluid-structure heat transfer simulation model and a turbine blade static simulation model. These two models are used to prepare for obtaining the turbine blade temperature field and stress field, respectively. The fluid-structure heat transfer simulation adopts a quasi-steady-state treatment. In the quasi-steady-state treatment, since the thermal settling time of the solid system is much longer than the flow settling time, the flow field calculation and solid field calculation are decoupled, and the two are transferred through temperature boundaries. The turbine blade fluid-structure heat transfer simulation model includes a turbine flow channel and a turbine blade model. The boundary conditions include the total temperature and pressure at the inlet of the main flow and the blade cooling channel, and the static pressure at the outlet of the turbine flow channel. The aforementioned turbine blade static simulation model includes a turbine blade model, and the loads are the temperature field heat, stress, and rotational speed calculated by the turbine blade fluid-structure heat transfer simulation model.

[0035] S140 represents the low-dimensional latent variable distribution of the Wasserstein variational autoencoder trained based on S120. Latin hypercube sampling is performed. Based on the Wasserstein variational autoencoder established in step S120, sample calculation point parameters are generated and used as inputs to the turbine blade fluid-structure heat transfer simulation model and turbine blade static simulation model in step S130. This yields turbine blade temperature and stress field sample sets. A reduced-order flow field model is constructed using the Orthogonal Eigenvalue Decomposition (POD) theory for the temperature and stress field sample sets. The Orthogonal Eigenvalue Decomposition (POD) theory assumption can be stated as: for any n-dimensional solution under arbitrarily varying inlet and outlet parameters... (where n is the number of nodes), can be represented by a set of basis functions as follows: (m is the number of basis functions); the method for selecting the basis functions is based on the principle of singular value decomposition, for a matrix... Then there exist two orthogonal matrices. and Make ,in This represents the contribution of each basis vector in V to the snapshot matrix, according to the tolerance requirements. The number of basis functions is determined by M, which is the same as m, and N is the number of samples in the sample set. The parts of the singular value decomposition process not described in detail above are well-known to those skilled in the art or can be understood based on existing technology, and will not be elaborated here. In this example, η is taken as 99.95%, and the first three order basis functions are obtained as basis functions.

[0036] S150, combining the solution space basis functions determined in step S140, obtain the boundary condition parameters - turbine blade temperature field dataset. Boundary condition parameters - turbine blade stress field dataset The coefficients of each solution expressed in terms of basis functions Construct a dataset of boundary condition parameters - turbine blade temperature field basis function coefficients. Boundary condition parameters - Turbine blade stress field basis function coefficients dataset ,in Boundary condition parameters; established using the radial basis function method. and The surrogate model is defined as follows: f is the mapping relationship between boundary condition parameters and turbine blade temperature field basis function coefficients, and g is the mapping relationship between boundary condition parameters and turbine blade stress field basis function coefficients.

[0037] In step S160, during service, the actually changing boundary condition parameters (including the total temperature and pressure at the turbine mains inlet, the total temperature and pressure at the cooling air inlet, the static pressure at the turbine mains outlet, and the rotational speed) are used as input to the surrogate model to obtain the reduced-order basis function coefficients (the basis function coefficients are 'a' from step S140). The basis functions are then linearly superimposed through eigenorthogonal decomposition to quickly obtain the turbine blade temperature and stress fields. The surrogate model is obtained in step S150. and Proxy model.

[0038] In summary, considering the characteristics of turbine blade simulation parameter changes during service, a low-dimensional latent variable distribution in a high-dimensional parameter space is learned using a deep learning generative model, the Wasserstein variational autoencoder. This latent variable distribution is then sampled to obtain turbine blade temperature and stress field sample sets. Based on this, a non-intrusive method based on orthogonal characteristic decomposition (POD) and radial basis functions (RBF) is employed to construct reduced-order models of the turbine blade temperature and load fields.

[0039] The technical solution of this invention is a method for constructing a reduced-order model of temperature / stress field that can take into account the high-dimensional parameters of turbine blade simulation, and is used for rapid calculation of temperature / stress field of turbine blade during service.

[0040] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0041] Although the invention has been described with respect to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of explaining or limiting the subject matter of the invention.

Claims

1. A method for constructing a reduced-order model of the temperature and stress fields of a turbine blade, characterized in that, include: Step S110: Obtain the change history of boundary condition parameters required for fluid-structure heat transfer simulation and static simulation of turbine blades during service. The boundary condition parameters include the total temperature and total pressure at the turbine main flow inlet, the total temperature and total pressure at the cooling airflow inlet, the static pressure at the turbine main flow outlet, and the rotational speed. S120 is divided into groups according to the range of rotational speed variation. Several points are extracted from each group. 70% of these points are selected to form the training set of the Wasserstein variational autoencoder, and 30% are selected to form the validation set of the Wasserstein variational autoencoder. The Wasserstein variational autoencoder is trained using a momentum-based stochastic gradient descent optimization algorithm. S130, establish a fluid-structure heat transfer simulation model and a static simulation model of the turbine blade; S140, Distribution of Low-Dimensional Latent Variables Latin hypercube sampling is performed. Based on the Wasserstein variational autoencoder established in step S120, the parameters of the sample calculation points are generated as inputs to the turbine blade fluid-structure heat transfer simulation model and turbine blade static simulation model in step S130. The turbine blade temperature field and stress field sample sets are obtained. The flow field reduced-order model of the temperature field sample set and stress field sample set is constructed using the intrinsic orthogonal decomposition theory. The solution space basis functions of the flow field reduced-order model are obtained. S150, combining the solution space basis functions determined in step S140, obtain the boundary condition parameters - turbine blade temperature field dataset. Boundary condition parameters - turbine blade stress field dataset The coefficients of each solution expressed in terms of basis functions Construct a dataset of boundary condition parameters - turbine blade temperature field basis function coefficients. Boundary condition parameters - Turbine blade stress field basis function coefficients dataset Dataset; established using the radial basis function method. and Proxy model, in which is the boundary condition parameter, f is the mapping relationship between the boundary condition parameter and the basis function coefficients of the turbine blade temperature field, and g is the mapping relationship between the boundary condition parameter and the basis function coefficients of the turbine blade stress field. During service, the S160 uses the actual changing parameters as input to the surrogate model to obtain the reduced-order basis function coefficients. The basis functions are then linearly superimposed through intrinsic orthogonal decomposition to obtain the reduced-order model of the turbine blade temperature field and stress field.

2. The method for constructing a reduced-order model of the temperature and stress fields of turbine blades according to claim 1, characterized in that, The parameters that actually change include the total temperature and pressure at the turbine mains inlet, the total temperature and pressure at the cooling air inlet, the static pressure at the turbine mains outlet, and the rotational speed.

3. The method for constructing a reduced-order model of the temperature and stress fields of turbine blades according to claim 1, characterized in that, The loss function of the Wasserstein variational autoencoder consists of two parts: reconstruction loss and regularization. The reconstruction loss uses the mean squared error loss, and its expression is as follows: , where x is the service parameter. Here, n is the number of encoder outputs, and the regularization uses the maximum average difference, expressed as: ， In the formula, Z|X is the probability distribution of the boundary condition parameters actually generated by the autoencoder model, Z|X is the conditional probability, and Q is the distribution of the latent variables in the actual output of the encoder. Here, we have a low-dimensional latent variable distribution, D is the divergence between the target and actual latent variable distributions, λ is a hyperparameter, X is the training parameters, G is the decoder output, c(X, G(Z)) represents the distance metric between the training parameters and the decoder output, and inf denotes the lower bound, with parameters below inf representing arbitrary parameters. The encoder is defined by the subscript X, which represents the training boundary condition parameters, and the subscript Z, which represents the latent variables of the boundary condition parameters after dimensionality reduction.

4. The method for constructing a reduced-order model of the temperature and stress fields of turbine blades according to claim 1, characterized in that, The fluid-structure heat transfer simulation model includes turbine flow channel and turbine blade model. The boundary conditions include the total temperature and pressure at the inlet of the main flow channel and the blade cooling channel, and the static pressure at the outlet of the turbine flow channel. The static simulation model includes turbine blade model. The loads are the temperature field heat, stress and rotational speed calculated by the heat transfer model.

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