Convolutional neural network based turbine damping blade dynamics design optimization method

Abstract

The application discloses a turbine damping blade dynamics design optimization method based on a convolutional neural network, comprising the following steps: obtaining a blade vibration reduction model, selecting model parameters and aerodynamic parameters to construct a characteristic space, calculating frequency response characteristics by using an arc length continuation method based on a multi-harmonic balance method, constructing a series of convolutional neural network models, normalizing characteristic parameters, frequency response characteristics and dynamic stress fields, and realizing vibration reduction performance optimization by combining automatic differentiation algorithms with characteristic prediction. The turbine damping blade dynamics design optimization method based on the convolutional neural network can realize accurate and rapid prediction of nonlinear response of the turbine damping blade, save calculation cost, improve solving efficiency, and obtain a friction damping structure scheme with the best vibration reduction effect in a given parameter working condition range, thereby providing theoretical support for dynamics design and optimization of turbine damping blades in engineering.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear dynamics design of turbine blades, and specifically relates to a dynamics design method for turbine damping blades based on convolutional neural networks. Background Technology

[0002] In the dynamic design of high-speed, high-power turbines, accurately predicting the dynamic behavior of blades is crucial for reducing the risk of high-cycle fatigue failure and designing robust turbine bladed disk systems. Severe vibrations of blades near the resonance point can generate excessive dynamic stress, leading to structural failure or even fracture.

[0003] Friction dampers are widely used in the vibration reduction design of turbine blades due to their simple structure and good vibration reduction effect. Common forms include damping bands, boss pull plates, blade root platform dampers, and wedge structures. They dissipate vibration energy through dry friction, effectively suppressing the vibration level of the blade and improving the safety and reliability of the structure.

[0004] However, friction-damped structures exhibit strong nonlinear characteristics. The dynamic analysis of damped blades requires solving complex sets of nonlinear partial differential equations with enormous degrees of freedom—tens of millions of degrees of freedom for a single-stage, full-cycle bladed disk vibration—resulting in high computational costs. Traditional nonlinear analysis methods are slow and exhibit poor convergence for strongly nonlinear problems, making it difficult to obtain unstable solutions. In some frequency bands, they may even fail to converge altogether, ultimately leading to solution failure.

[0005] In addition, blade dynamics design requires studying the mapping relationship between vibration response, friction, and design conditions. Direct analysis through design parameters requires repeatedly solving the same nonlinear partial differential equation system under different conditions. As the number of variables to be studied increases, the amount of computation increases exponentially, which greatly increases the computational cost and makes it difficult to meet the needs of nonlinear dynamics design and vibration reduction optimization in engineering. Summary of the Invention

[0006] The purpose of this invention is to provide a dynamic design optimization method for turbine damping blades based on convolutional neural networks. By constructing a complete mapping from characteristic parameters to frequency response characteristics and further to dynamic stress field distribution, it achieves accurate and rapid prediction of the nonlinear dynamic characteristics of turbine damping blades, saves computational costs, improves solution efficiency, and obtains the friction damping structure scheme with the best vibration reduction effect within a given parameter operating condition range, thus providing theoretical support for the dynamic design of turbine machinery in engineering.

[0007] To achieve the above objectives, this invention discloses a method for dynamic design optimization of turbine damping blades based on convolutional neural networks, comprising the following steps:

[0008] S1. Model establishment and parameter sampling: The degrees of freedom of the turbine shroud damped blade model are reduced, a friction damping model is established for the shroud contact surface, and a feature space is constructed for the model parameters and aerodynamic parameters to achieve parameter selection.

[0009] S2. Solve the dynamic characteristics of the model. Using the arc length extension method based on the multi-harmonic balance method, and according to the parameters of the reduced model and characteristic space, complete the response characteristics analysis of the blade under multiple modes. Reconstruct the stress field based on the calculated data and the dynamic inversion method.

[0010] S3. Construct a series of convolutional neural network models, use a deep convolutional neural network model to construct a frequency response characteristic prediction network, use a U-net convolutional neural network model to construct a dynamic stress field reconstruction network, and connect the two neural networks.

[0011] S4. Network model training and validation: Normalize the feature parameters, frequency response characteristics and dynamic stress field, divide the dataset into training set and validation set, use the training set data to train the network model, realize the complete mapping from feature parameters to frequency response characteristics to dynamic stress field, and finally validate the accuracy of frequency response characteristics and dynamic stress field prediction.

[0012] S5. Characteristic prediction and optimization: Based on different feature parameters, the trained network model can quickly and accurately predict frequency response characteristics and corresponding dynamic stress fields; at the same time, it combines the automatic differentiation algorithm in deep learning to achieve efficient vibration reduction performance optimization in order to obtain the best parameters.

[0013] Preferably, in step S1, a finite element analysis model of the vibration characteristics of the entire turbine shroud damped blade and the wheel disk is established, a friction damping model is established between the contact surfaces of adjacent blade shrouds, and the finite element model of the entire blade is reduced by the modal reduction method, while reasonably retaining the number of principal modes.

[0014] To consider the nonlinear dynamic characteristics of the blade, model parameters (contact stiffness K) are selected. x (Friction coefficient μ, normal force N0) and aerodynamic parameters (excitation force amplitude F) ex Excitation frequency ω e Initial phase As design parameters, given the range of values ​​for each design parameter, and using the Latin Hypercubic Sampling method to uniformly sample n sets of data, a characteristic parameter space for the design and optimization of turbine blade damping structures is established. Where K x ∈[K xmin ,K xmax ], μ∈[μ min ,μ max ], N0∈[N 0min N 0max], F e ∈[F emin ,F emax ],ω e ∈[ω emin ,ω emax ],

[0015] Preferably, in step S2, the finite element analysis method is used to perform modal analysis on the reduced model to obtain the blade modal information (modal shape matrix B, modal stress matrix σ) under each set of parameter conditions. m The arc-length extension method based on the multi-harmonic balance method was used to solve the nonlinear vibration characteristics of the reduced model, and the frequency response characteristics of the blade's multi-mode under various parameter conditions were obtained (frequency response curve of tangential relative displacement of the shroud contact surface f(A,ω), and frequency response curve of tangential relative displacement versus tangential friction f(F)). c ,x rel The calculated blade modal information and vibration characteristic data are input into the dynamic stress inversion algorithm to reconstruct the blade dynamic stress and obtain the analysis results of the maximum dynamic stress of the blade under various parameter conditions.

[0016] Preferably, in step S3, the convolutional neural network model consists of two convolutional neural network models, which can be divided into a frequency response characteristic prediction network and a dynamic stress field reconstruction network, written as:

[0017]

[0018]

[0019] in Indicates the characteristic parameters Frequency response characteristics The mapping relationship corresponds to the frequency response characteristic prediction network, where Θ1 represents the network parameters. This indicates that the frequency response characteristics Reconstructing the dynamic stress field The mapping relationship corresponds to the dynamic stress field reconstruction network, where Θ2 represents the network parameters.

[0020] Preferably, the first frequency response characteristic prediction deep convolutional neural network model includes an input layer, a fully connected layer, a convolutional layer, a pooling layer, and an output layer. The model realizes the prediction of frequency response characteristics from various feature parameters.

[0021] The second dynamic stress field reconstruction network is constructed using the U-net architecture. This network can reconstruct the dynamic stress field based on existing frequency response characteristics. Reconstructing the dynamic stress field The function here refers to the frequency response characteristics, which can be either real or predicted.

[0022] Preferably, in step S4, the input and output parameters of the above-sampled n groups are normalized respectively. For the input variables:

[0023]

[0024] Where max and min represent the maximum and minimum values ​​of the parameters, respectively, and the input variables correspond to the feature space model parameters and aerodynamic parameters;

[0025] For the output variables, i.e., for the specified model in terms of frequency response characteristics and dynamic stress field, the calculated data is first interpolated to obtain output data of length 512, which is then further normalized to obtain:

[0026]

[0027] The normalized dataset was divided into training and validation sets to complete the training data preprocessing; the loss function for both network models was selected as MSE, and the optimizer used in the network model training was Adam.

[0028] Preferably, in step S5, the trained convolutional neural network model can be used to quickly and accurately predict the frequency response characteristics and dynamic stress field of the physical model, thereby significantly reducing the computational cost required to solve the high-fidelity finite element model; further, the automatic differentiation algorithm in deep learning is combined to achieve rapid optimization of the objective function; based on the complete mapping relationship between the feature parameters to the frequency response characteristics to the dynamic stress field constructed by the convolutional neural network model, the frequency response characteristics and dynamic stress field distribution under each feature parameter can be obtained while optimizing efficiently, capturing the relationship between the physical field and the performance parameters.

[0029] Therefore, this invention proposes an analysis and design method based on convolutional neural networks, with the following specific technical effects:

[0030] (1) The convolutional neural network model established by this invention can establish a proxy model of the corresponding dynamic characteristics after one sampling. After the network training is completed, it can greatly reduce the time spent on analyzing the dynamic characteristics of the blade and achieve accurate prediction of the dynamic characteristics.

[0031] (2) The convolutional neural network of the present invention consists of two parts, which respectively realize the functions of frequency response characteristic prediction and dynamic stress field reconstruction, and can realize the complete mapping from feature parameters to frequency response characteristics and further to dynamic stress field distribution. Among them, the dynamic stress field reconstruction network adopts the U-net convolutional neural network model. This network splices together signals of the same length in the contraction and expansion parts, which can help the network learn the information in the blade frequency response characteristics better and improve the training effect of the dynamic stress field reconstruction network.

[0032] (3) The present invention utilizes an automatic differentiation algorithm to help efficiently capture the global optimal solution, reduce the number of iterations required in the optimization process, and improve optimization efficiency.

[0033] (4) The fully mapped convolutional neural network of the present invention can improve the interpretability of the optimization results. Traditional surrogate models such as ANN and SVR only establish the mapping relationship between feature parameters and performance, and cannot interpret the physical meaning of the optimization results. The frequency response characteristics and dynamic stress field output by the network of the present invention can interpret the vibration reduction optimization results according to the physical meaning.

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of a turbine damping blade dynamic design optimization method based on a convolutional neural network according to an embodiment of the present invention.

[0036] Figure 2 This is a schematic diagram of the finite element analysis model of the vibration characteristics of the entire turbine damping blade and the wheel disk according to an embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of a friction damping contact model according to an embodiment of the present invention;

[0038] Figure 4 This is a schematic diagram of the characteristic parameter space for the design optimization of the turbine blade damping structure according to an embodiment of the present invention: (a) model parameter space; (b) aerodynamic parameter space;

[0039] Figure 5 This is a schematic diagram of the dynamic stress reconstruction method according to an embodiment of the present invention;

[0040] Figure 6 This is a schematic diagram of the convolutional neural network used in an embodiment of the present invention;

[0041] Figure 7 This is a graph of the loss function obtained from training in an embodiment of the present invention;

[0042] Figure 8 This is a comparison chart of the frequency response characteristic network prediction results implemented in this invention. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0045] Figure 1 This is a flowchart of a turbine damping blade dynamics design optimization method based on convolutional neural networks. The specific steps are as follows:

[0046] The first step is model establishment and parameter sampling. The degrees of freedom of the turbine shroud damped blade model are reduced, a friction damping model is established for the shroud contact surface, and parameter selection is performed to construct a feature space for the model parameters and aerodynamic parameters.

[0047] In the first step, a finite element analysis model of the vibration characteristics of the entire turbine shroud damped blade and the turbine disk is established. A friction damping model is established between the contact surfaces of adjacent blade shrouds. The modal reduction method is used to reduce the finite element model of the entire blade and reasonably retain the number of principal modes.

[0048] To consider the nonlinear dynamic characteristics of the blade, model parameters (contact stiffness K) are selected. x (Friction coefficient μ, normal force N0) and aerodynamic parameters (excitation force amplitude F) ex Excitation frequency ω e Initial phase As design parameters, the range of values ​​for each design parameter is given, and the Latin Hypercubic Sampling method is used for uniform sampling to establish the characteristic parameter space for the design and optimization of turbine blade damping structures. Where K x ∈[K xmin ,K xmax ], μ∈[μ min ,μ max ], N0∈[N 0min N 0max ], F e ∈[F emin ,F emax ],ω e ∈[ω emin ,ω emax ],

[0049] The second step is to solve the dynamic characteristics of the model. Using the arc length extension method based on the multi-harmonic balance method, the response characteristics of the blade under multiple modes are analyzed according to the parameter inputs of the reduced model and characteristic space. The stress field is reconstructed by combining the calculated data with the dynamic inversion method.

[0050] In the second step, the finite element analysis method is used to perform modal analysis on the reduced model to obtain the blade modal information (modal shape matrix B, modal stress matrix σ) under each set of parameter conditions. m The arc-length extension method based on the multi-harmonic balance method was used to solve the nonlinear vibration characteristics of the reduced model, and the frequency response characteristics of the blade's multi-mode under various parameter conditions were obtained (frequency response curve of tangential relative displacement of the shroud contact surface f(A,ω), and frequency response curve of tangential relative displacement versus tangential friction f(F)). c ,x rel The calculated blade modal information and vibration characteristic data are input into the dynamic stress inversion algorithm to reconstruct the blade dynamic stress and obtain the analysis results of the maximum dynamic stress of the blade under various parameter conditions.

[0051] The third step is to construct a series of convolutional neural network models. A frequency response characteristic prediction network is constructed using a deep convolutional neural network model, and a dynamic stress field reconstruction network is constructed using a U-net convolutional neural network model. The two neural networks are then connected.

[0052] In the third step, the convolutional neural network model consists of two convolutional neural network models, which can be divided into a frequency response prediction network and a dynamic stress field reconstruction network, written as:

[0053]

[0054]

[0055] in Indicates the characteristic parameters Frequency response characteristics The mapping relationship corresponds to the frequency response characteristic prediction network, where Θ1 represents the network parameters. This indicates that the frequency response characteristics Reconstructing the dynamic stress field The mapping relationship corresponds to the dynamic stress field reconstruction network, where Θ2 represents the network parameters.

[0056] The first deep convolutional neural network model for frequency response prediction includes an input layer, fully connected layers, convolutional layers, pooling layers, and an output layer. The model predicts frequency response characteristics from various feature parameters. For the input feature parameters, the variable dimension is 1×9. After passing through a fully connected layer, the data dimension is transformed to 1×2048. Then, after multiple convolutional, activation, and pooling processes, the data is expanded to a length of 512, thus predicting the response characteristics at frequencies of 512.

[0057] The second dynamic stress field reconstruction network is constructed using the U-net architecture. This network can reconstruct the dynamic stress field based on existing frequency response characteristics. Reconstructing the dynamic stress field The function here refers to the frequency response characteristics, which can be real or predicted. The network can be divided into a shrinking path and an expanding path. In the shrinking path, multiple convolution operations are used to transform the 1×512-dimensional frequency response characteristic data into a 512×2-dimensional dimension. In the expanding path, multiple deconvolution operations are used to change the data length, and the signals in the shrinking path of the corresponding length are spliced ​​together. Finally, an upsampling process is used to transform the data dimension into a 1×512-dimensional dimension, which corresponds to the reconstructed dynamic stress field.

[0058] The fourth step is network model training and validation. The feature parameters, frequency response characteristics, and dynamic stress field are normalized, and the dataset is divided into training and validation sets in a 7:3 ratio. The network model is trained using the training set data to achieve a complete mapping from feature parameters to frequency response characteristics to dynamic stress field. Finally, the accuracy of the frequency response characteristics and dynamic stress field predictions is validated.

[0059] The fifth step is characteristic prediction and optimization. Based on different feature parameters, the trained network model can quickly and accurately predict frequency response characteristics and corresponding dynamic stress fields. At the same time, it combines the automatic differentiation algorithm in deep learning to achieve efficient vibration reduction performance optimization and obtain the best parameters.

[0060] In the fourth step, the n samples are normalized for both the input and output parameters. For the input variables:

[0061]

[0062] Where max and min represent the maximum and minimum values ​​of the parameters, respectively, and the input variables correspond to a total of 6 parameters, including the feature space model parameters and aerodynamic parameters.

[0063] For the output variables, that is, for the specified model in terms of frequency response characteristics and dynamic stress field, the calculated data are first interpolated to obtain output data of length 512, and then further normalized to obtain:

[0064]

[0065] The normalized data was divided into training and validation sets in a 7:3 ratio to complete the training data preprocessing. The loss function for both network models was MSE, and a mini-batch size of 64 samples was used for training. The Adam optimizer was used for network model training. The initial learning rate was set to 0.003 for the first 100 steps, and then reduced to 0.1 every 50 steps. Training was completed after 300 steps.

[0066] The trained convolutional neural network model enables rapid and accurate prediction of the frequency response characteristics and dynamic stress field of physical models, significantly reducing the computational cost required for solving high-fidelity finite element models. Furthermore, it combines automatic differentiation algorithms from deep learning to achieve rapid optimization of the objective function. Based on the complete mapping relationship between feature parameters, frequency response characteristics, and dynamic stress field constructed by the convolutional neural network model, the model can efficiently optimize while obtaining the frequency response characteristics and dynamic stress field distribution under each feature parameter, capturing the relationship between the physical field and performance parameters.

[0067] Figure 2 The figure shows a finite element analysis model of the vibration characteristics of a complete turbine damping blade and disk with a shroud structure established according to an embodiment of the present invention. It consists of 30 blades and a corresponding disk, and the entire model is meshed using hexahedral elements, comprising 129,960 elements and 137,857 nodes. Modal reduction was used to reduce the finite element model of the complete blade, retaining the first 300 vibration modes as the principal degrees of freedom. Under airflow excitation, relative motion occurs between the shrouds of adjacent blades, which can be divided into two components: parallel contact surface and perpendicular contact surface. An excessively large relative motion component perpendicular to the contact surface can cause shroud contact surface separation, resulting in more complex and strongly nonlinear blade vibration characteristics. Considering the frictional damping between the shrouds, multiple point-to-point slip-viscous frictional damping contact models were established at the shroud contact surface. For ease of calculation, the total normal pressure between the contact surfaces was evenly distributed to each established contact model. Under high-speed rotation, the dissipation of blade vibration energy mainly comes from the friction between the blade shrouds. Due to the large centrifugal force of the blade, there is strong coupling between the blade root and the disk. Therefore, the friction at the blade root can be ignored, and the blade root contact surface is coupled to the disk. The blade shroud contact surface is parallel to the axial direction of the disk, and the normal direction of the shroud contact surface is the circumferential direction of the blade-disk model.

[0068] Figure 3 The diagram shows the friction damping contact model and its hysteresis loop constructed according to an embodiment of the present invention. When the turbine damping blade is operating normally, the normal pressure between the damping structures can be considered as a constant value N0. Therefore, the contact state of the entire contact surface can be simplified to a contact unit containing two points (i.e., it is assumed that the nodes on the entire contact surface are in the same motion state), and each contact unit has the same contact parameters. Based on the above assumptions, the tangential dry friction force F between the damping structures...

[0069] c can be expressed in the form of equation (1):

[0070]

[0071] In the formula: F ci K represents the tangential frictional force (N) on the contact surface of the i-th pair of contact units. xTangential stiffness at the contact surface / N·m -1 μ is the coefficient of friction of the contact surface; N0 is the normal pressure applied to the contact surface in N; x i (τ) represents the relative displacement (in meters) between the two nodes of the i-th contact pair at time τ, which is in the viscous phase; x i (τ stk ) represents the first initial viscous time τ before that specific moment τ. stk The corresponding relative displacement between nodes / m; The moment τ is the beginning of the slip phase. slp Relative velocity between two nodes / m·s -1 The symbol sgn(﹒) represents the symbol for taking the item within the parentheses.

[0072] The relative motion, viscosity, and slippage states between two nodes need to be determined through the relationship between the tangential friction force and the threshold μN0. For the viscous state, it is assumed that when the relative motion between the two nodes stops or reverses, the motion state of the contact surface completes the transition from slippage to viscosity, i.e.:

[0073] Slip → Viscosity (2)

[0074] In the formula, τ stk,l The generalized time / rad preceding the start of the viscous phase. From the viscous time τ stk The time τ from the start of the next slip phase slp This stage is the viscous stage shown in equation (3). Furthermore, the transition time τ from viscous to slip state after viscosity... slp We obtain it from the following formula:

[0075] |K x (x(τ sl )-x(τ st ))|>μN0 Viscosity→Slip (3)

[0076] Figure 4 The diagram shows the characteristic parameter space for turbine blade damping structure design optimization established in this embodiment of the invention: (a) model parameter space; (b) aerodynamic parameter space. A sample space is formed by randomly selecting 1000 parameter points within a given range for each characteristic parameter using the Latin hypercube sampling method. The range of each characteristic parameter is: K x ∈[500,1500]N / mm, μ∈[0.15,0.45], N0∈[1,1000]N, F e ∈[1,10]N,ω e ∈[50,200]Hz,

[0077] Figure 5The diagram shows a schematic of the dynamic stress reconstruction method. For a blade-disc system with a friction-damped structure, its dynamic equation can be expressed as:

[0078]

[0079] In the formula, M, C, and K are the mass, damping, and stiffness matrices, respectively. The displacement, velocity, and acceleration vectors of the forced vibration response of all blades, F c Let P(t) be the frictional force vector of the contact surface of the belt, P(t) be the excitation force vector, and t be the time variable. The forced vibration response of the j-th node in x(t) can be expressed in the form of a superposition of moving modes:

[0080]

[0081] In the formula x j (t) represents the forced vibration response of the j-th node, φ kj Let η be the displacement of the j-th node in the k-th mode. k (t) represents the coordinates of the k-th mode, and m is the mode order. Equation (5) can be expressed in matrix form:

[0082] x(t)=Bη(t) (6)

[0083] In the formula, B is the mode shape matrix, and η(t) is the modal coordinate vector. The matrix B and vectors x(t) and η(t) in the formula have the following forms:

[0084] x(t) = [x1(t), x2(t), ..., x N (t)] T (7)

[0085]

[0086] η(t)=[η1(t),η2(t),L,η N (t)] T (9)

[0087] In equations (7) to (9), N is the number of blades.

[0088] Among them, the blade vibration response vector x(t) is obtained by nonlinear vibration characteristic analysis, and the mode shape matrix B is calculated by the finite element method for the blade-disk reduced model. Therefore, according to equation (6), the modal coordinate vector η(t) can be obtained by the inverse matrix operation of B:

[0089] η(t)=B -1 x(t) (10)

[0090] In the formula B -1Let be the generalized inverse matrix of B.

[0091] From equation (5), the strain at the j-th node can be expressed as:

[0092]

[0093] In the formula ε kj Let be the strain at the j-th node in the k-th mode. When all nodal strains are expressed as vectors, we have:

[0094]

[0095] In the formula ε k Let be the k-th strain mode vector of the blade, with elements ε. kj When a node represents the same node at the same position for all leaves, ε k The number of elements equals the total number of blades. The k-th stress mode vector σ k It can be derived from the k-th order strain mode vector ε k Calculation yielded:

[0096] σ k =D e ε k (13)

[0097] In the formula, D e D is the strain-stress transformation matrix. e and ε k It can be obtained by calculation using the finite element method. σ k Consider them as column vectors, and treat all m-order column vectors σ as column vectors. k Combined to form the modal stress matrix σ m :

[0098] σ m =[σ1,σ2,L,σ m (14)

[0099] According to the modal superposition theory, the dynamic response of a structure can be represented by a superposition of modal coordinate bases. Once the modal coordinate vector η(t) is obtained, the dynamic stress of the system can be obtained as follows:

[0100] σ D (t)=σ m η(t) (15)

[0101] In the formula σ D (t) is the dynamic stress vector of the system.

[0102] When the blade tip displacement reaches its maximum amplitude (at which point t = t0), it is assumed that the stress at a certain point on the blade also reaches its maximum value. Assuming the bladed disk is harmonic, all blades have the same maximum stress level at the same location on each blade. Assuming Node A is the point with the maximum dynamic stress among all points on the blade, the maximum dynamic stress of the blade is the dynamic stress at point Node A at t = t0, and it is expressed by the following formula:

[0103] σ Dmax =σ(t0) (16)

[0104] x max =x(t0) (17)

[0105] In the formula σ Dmax and x max Let x be the maximum dynamic stress of the blade and the blade tip displacement at t = t0, respectively. From equations (10) to (17), the dynamic stress vector of the blade during vibration response can be obtained from the blade tip displacement vector x. max Calculation yielded:

[0106] σ Dmax =σ m η = σ m B -1 x max (18)

[0107] Based on this analysis and derivation, a method for reconstructing the dynamic stress of the harmonic bladed disk vibration response was realized by obtaining the nonlinear response of the blade.

[0108] Figure 6 This is a schematic diagram of the convolutional neural network structure used in an embodiment of the present invention. The overall network can be divided into two networks: a frequency response prediction network and a dynamic stress field reconstruction network. The frequency response prediction network uses a deep convolutional neural network to predict the frequency response curve based on the feature parameters. This network first uses a fully connected neural network to transform the six feature parameters into a 1×2048 dimension. Then, after multi-layer convolution, activation, and pooling operations, it finally unfolds to obtain a frequency response distribution of length 512, achieving efficient prediction of the frequency response characteristics. The dynamic stress field reconstruction network is also a convolutional neural network, implemented using the U-net architecture. This network consists of a contraction path and an expansion path. The contraction path uses a multi-layer convolutional neural network to convolve the frequency response data dimension to a size of 512×2. The expansion path uses a deconvolutional neural network, and the corresponding length data of the contraction path is concatenated with that of the expansion path. Finally, an upsampling step is used to obtain a 1×512 dynamic stress field distribution.

[0109] Figure 7The graph shows the change of the training loss function with the number of iterations. The solid line represents the loss function calculated on the training set, and the dashed line represents the loss function calculated on the validation set. The loss functions of both the training and validation sets decrease continuously with the number of iterations. When the number of iterations reaches 200, the loss functions of both the training and testing sets decrease to 1e. -4 Orders of magnitude. After 200 iterations, the learning rate was reduced to 0.1 times its original value, and the loss function of the training set was further reduced to 1e. -5 The loss function of the validation set data is reduced by orders of magnitude and remains relatively stable, which can be regarded as the completion of the frequency response characteristic network training.

[0110] Figure 8 This is a comparison chart of the frequency response characteristic prediction results obtained by the convolutional neural network. The scatter points represent the actual values, and the curves represent the predicted frequency response characteristic curves. The comparison shows that the frequency response characteristic curves predicted by the convolutional neural network are very close to the actual frequency response characteristic points. It can accurately capture the peak values ​​of each amplitude of the frequency response characteristic curve and their corresponding frequency parameters. It can efficiently replace high-fidelity finite element models, enabling rapid prediction and analysis of the dynamic characteristics of complex turbine damping models, thereby accelerating the optimization of model dynamic design.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the embodiments of the present invention have been described in detail with reference to the above embodiments, those skilled in the art can still make modifications or equivalent substitutions to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are within the protection scope of the claims of the present invention pending approval.

Claims

1. A method for dynamic design optimization of turbine damping blades based on convolutional neural networks, characterized in that: S1. Model establishment and parameter sampling: The degrees of freedom of the turbine shroud damped blade model are reduced, a friction damping model is established for the shroud contact surface, and a feature space is constructed for the model parameters and aerodynamic parameters to achieve parameter selection. S2. Solve the dynamic characteristics of the model. Using the arc length extension method based on the multi-harmonic balance method, and according to the parameters of the reduced model and characteristic space, complete the response characteristics analysis of the blade under multiple modes. Reconstruct the stress field based on the calculated data and the dynamic inversion method. S3. Construct a series of convolutional neural network models, use a deep convolutional neural network model to construct a frequency response characteristic prediction network, use a U-net convolutional neural network model to construct a dynamic stress field reconstruction network, and connect the two neural networks. S4. Network model training and validation: The feature parameters, frequency response characteristics, and dynamic stress field are normalized. The dataset is divided into a training set and a validation set. The network model is trained using the training set data to achieve a complete mapping from feature parameters to frequency response characteristics to dynamic stress field. Finally, the accuracy of the frequency response characteristics and dynamic stress field predictions is validated. The series of convolutional neural network models are configured to achieve a complete mapping from feature parameters to frequency response characteristics to dynamic stress field. S5. Characteristic prediction and optimization: Based on different feature parameters, the trained network model can quickly and accurately predict frequency response characteristics and corresponding dynamic stress fields; at the same time, it combines the automatic differentiation algorithm in deep learning to achieve efficient vibration reduction performance optimization in order to obtain the best parameters. In step S3, the convolutional neural network model consists of two convolutional neural network models: a frequency response prediction network and a dynamic stress field reconstruction network, written as: in, Indicates the characteristic parameters Frequency response characteristics The mapping relationship corresponds to the frequency response characteristic prediction network. Indicates network parameters; This indicates that the frequency response characteristics Reconstructing the dynamic stress field The mapping relationship corresponds to the dynamic stress field reconstruction network. This represents the network parameter.

2. The method for dynamic design optimization of turbine damping blades based on convolutional neural networks according to claim 1, characterized in that: In step S1, a finite element analysis model of the vibration characteristics of the entire turbine shroud damped blade and the wheel disk is established. A friction damping model is established between the contact surfaces of adjacent blade shrouds. The modal reduction method is used to reduce the finite element model of the entire blade and reasonably retain the number of principal modes. To address the nonlinear dynamic characteristics of the blade, model parameters including contact stiffness are used. K x coefficient of friction μ Positive pressure N 0, and also aerodynamic parameters including excitation force amplitude. F ex Excitation frequency ω e Initial phase As design parameters, the range of values ​​for each design parameter is given, and n sets of data are uniformly sampled using the Latin Hypercubic Sampling method to establish the characteristic parameter space for the design and optimization of turbine blade damping structures. ,in , , , , , .

3. The method for dynamic design optimization of turbine damping blades based on convolutional neural networks according to claim 1, characterized in that: In step S2, the finite element analysis method is used to perform modal analysis on the reduced model to obtain the blade modal information under each set of parameter conditions; the arc length extension method based on the multi-harmonic balance method is used to solve the nonlinear vibration characteristics of the reduced model to obtain the frequency response characteristics of the multi-mode blade under each set of parameter conditions; the calculated blade modal information and vibration characteristic data are input into the dynamic stress inversion algorithm to reconstruct the blade dynamic stress and obtain the analysis results of the maximum dynamic stress of the blade under each parameter condition.

4. The method for dynamic design optimization of turbine damping blades based on convolutional neural networks according to claim 1, characterized in that: The frequency response characteristic prediction network is the first deep convolutional neural network model for frequency response characteristic prediction, including an input layer, a fully connected layer, a convolutional layer, a pooling layer, and an output layer. The model realizes the prediction of frequency response characteristics from various feature parameters. The second dynamic stress field reconstruction network is constructed using the U-net form. This network realizes the reconstruction of the frequency response characteristics based on the existing frequency response characteristics. Reconstructing the dynamic stress field The function.

5. The method for dynamic design optimization of turbine damping blades based on convolutional neural networks according to claim 1, characterized in that: In step S4, the input and output parameters of the above-sampled n groups are normalized respectively. For the input variables, we have: Where max and min represent the maximum and minimum values ​​of the parameters, respectively, and the input variables correspond to the feature space model parameters and aerodynamic parameters; For the output variables, i.e., for the specified model in terms of frequency response characteristics and dynamic stress field, further normalization yields: The normalized dataset was divided into training and validation sets to complete the training data preprocessing; the loss function for both network models was selected as MSE, and the optimizer used in the network model training was Adam.

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