Multi-agent model synchronous simulation method and device

Abstract

The embodiment of the invention provides a multi-agent model synchronous simulation method and device for random mistuned bladed disc probability flutter assessment, and the method comprises the steps: decomposing a fluid-solid coupling vibration model into a modal aerodynamic coefficient model of a fluid domain and a blade frequency mistuning quantity model of a solid domain; establishing a fluid domain multi-channel blade grid runner grid model and a solid domain blade finite element model; extracting a predetermined number of input samples; respectively completing deterministic analysis on a fluid domain and a solid domain through fluid mechanics simulation and solid dynamics simulation; respectively constructing a modal aerodynamic coefficient model and a blade frequency detuning quantity model through the training data and the test data; and proxy model simulation is carried out based on the modal aerodynamic coefficient model and the blade frequency detuning amount model, characteristic value response of the detuning bladed disc rotor system is obtained, and random detuning bladed disc probability flutter evaluation is carried out.

Description

Technical Field

[0001] This document relates to the field of probabilistic flutter assessment technology for stochastic detuned bladed disks, and in particular to a multi-agent model synchronous simulation method and device for probabilistic flutter assessment of stochastic detuned bladed disks. Background Technology

[0002] In practical engineering, due to differences in processing errors, wear, material properties, and installation conditions, turbomachinery blades are not entirely identical, and turbomachinery is often not perfectly harmonic, but rather detuned. For turbomachinery flutter problems, detuning can improve the aeroelastic stability of the oscillating blade cascade to a certain extent, which is beneficial for suppressing flutter. Therefore, a large amount of research has been conducted both domestically and internationally on the problem of detuned turbomachinery flutter. However, most of these studies are based on deterministic analysis methods and assume that the aerodynamic forces acting on the turbomachinery blades are deterministic. In fact, both the influencing factors of aerodynamic forces and the blade detuning parameters have significant uncertainties. To assess the impact of this uncertainty on detuned turbomachinery flutter, it is necessary to perform uncertainty prediction for turbomachinery flutter considering random detuning.

[0003] Currently, various uncertainty analysis methods have been developed for predicting the flutter uncertainty of tuned turbomachinery, mainly divided into robust aeroelastic analysis and probabilistic aeroelastic analysis. Robust aeroelastic analysis, primarily based on the bounded uncertainty assumption, analyzes the flight boundary where the stability margin is minimized under uncertainty, making it difficult to accurately characterize the stochastic nature of flutter behavior. Probabilistic aeroelastic analysis abandons the conventional stability boundary and replaces it with the concept of risk assessment, mainly using the direct Monte Carlo (MC) method to obtain the probability distribution characteristics of the flutter response, thereby quantifying the risk of flutter failure. Since the direct Monte Carlo (MC) method requires extensive numerical simulation experiments, and considering the high computational cost of fluid-structure interaction simulations involving complex nonlinear fluid / solid dynamics interactions, probabilistic aeroelastic analysis often uses surrogate models to replace complex numerical simulations, thus reducing the computational burden of the direct MC method.

[0004] However, unlike the flutter probability prediction problem of harmonic turbomachinery, in the flutter probability prediction problem of turbomachinery considering random detuning, the vibration characteristics of each blade on the detuned impeller rotor are different, which destroys the cyclic symmetry of the impeller rotor. Therefore, unlike harmonic turbomachinery, flutter probability analysis cannot be performed only for the most unstable traveling wave mode of the impeller rotor. Instead, the influence of all blade detuning on the aeroelasticity of the entire impeller rotor system under each mode needs to be considered simultaneously, so as to perform flutter probability analysis on the entire impeller rotor, resulting in a significant increase in computational cost.

[0005] In this context, to simplify calculations, existing probabilistic flutter assessment methods for stochastic detuned bladed disks often treat aerodynamic forces as deterministic variables or assume that aerodynamic forces follow a definite distribution characteristic, making it difficult to guarantee the accuracy of the assessment.

[0006] Currently, there is no feasible solution for conducting high-precision and high-efficiency probabilistic flutter assessment of stochastic detuned bladed disks, considering both aerodynamic factors and blade mistuning parameters.

[0007] In summary, during the process of realizing this invention, the inventors discovered at least the following problems in the prior art: If the Monte Carlo (MC) method is used directly for probabilistic analysis, the aerodynamic coupling effect of blade vibration and the coupling effect between the detuned blade and the flow field must be considered simultaneously. This requires a large number of fluid-structure interaction vibration simulations of the detuned bladed disk rotor, which consumes a lot of computational resources and seriously affects computational efficiency.

[0008] However, if the probability analysis is performed directly using the surrogate model method, it is difficult to meet the requirements of computational accuracy for the following reasons: (1) The direct surrogate model simulation severs the coupling between the fluid domain and the solid domain, and loses a lot of fluid-structure interaction information, making it difficult to reflect the influence of random detuning on the turbomachinery flutter from a mechanistic perspective; (2) Turbomachinery detuning makes the interaction between blade vibration and the surrounding flow field more complex, and the nonlinearity between the output response and the input random variables is higher, making it difficult for the direct surrogate model to approximate this highly nonlinear mapping relationship; (3) The detuning parameters of each blade on the detuned impeller rotor are different, which greatly increases the number of random variables in the probability analysis, and the direct surrogate model is prone to overfitting. Summary of the Invention

[0009] The purpose of this invention is to provide a multi-agent model synchronous simulation method and apparatus for assessing probabilistic flutter of stochastic detuned bladed disks, aiming to solve the above-mentioned problems in the prior art.

[0010] This invention provides a multi-agent model synchronous simulation method for assessing probabilistic flutter of stochastic detuned bladed disks, comprising: Based on the dynamic model of the detuned bladed disk rotor, the fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain, and the input random variables of the two models are determined. A multi-channel blade cascade mesh model in the fluid domain and a blade finite element model in the solid domain are established to perform deterministic analysis in the fluid domain and solid domain and obtain the output response. Based on the distribution characteristics of the influencing factors of modal aerodynamic coefficients and blade frequency mistuning, a predetermined number of input samples are extracted by Latin hypercube sampling. For the input samples, deterministic analysis of the fluid domain and solid domain is completed by fluid dynamics simulation and solid dynamics simulation, respectively, and training data and test data for surrogate modeling of fluid domain and solid domain are constructed. Using the LM-optimized vector surrogate model and the particle swarm optimization least squares support vector regression surrogate model, modal aerodynamic coefficient model and blade frequency detuning model are constructed respectively using training data and test data; By performing surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model respectively, the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain are obtained. The modal aerodynamic coefficient response and the blade frequency detuning response are then input into the vibration equation of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue response of the detuned bladed disk rotor system and performing probabilistic flutter assessment of the random detuned bladed disk.

[0011] This invention provides a multi-agent model synchronous simulation device for assessing probabilistic flutter of stochastic detuned bladed disks, comprising: The decomposition analysis module is used to decompose the fluid-structure interaction vibration model into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain based on the dynamic model of the detuned bladed disk rotor, and to determine the input random variables of the two models; to establish a multi-channel blade cascade mesh model in the fluid domain and a finite element model of the blade in the solid domain, to perform deterministic analysis in the fluid domain and solid domain, and to obtain the output response; The extraction and analysis module is used to extract a predetermined number of input samples based on the distribution characteristics of the influencing factors of modal aerodynamic coefficients and blade frequency mistuning, respectively, through Latin hypercube sampling; for the input samples, deterministic analysis of the fluid domain and solid domain is completed through fluid dynamics simulation and solid dynamics simulation, respectively, and training data and test data for modeling proxy models of the fluid domain and solid domain are constructed. The module is used to construct modal aerodynamic coefficient models and blade frequency mistuning models using LM-optimized vector surrogate models and particle swarm optimization least squares support vector regression surrogate models, respectively, through training and testing data. The simulation solution module is used to perform surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model, respectively, to obtain the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain. The modal aerodynamic coefficient response and the blade frequency detuning response are then input into the vibration equation of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue response of the detuned bladed disk rotor system and performing probabilistic flutter assessment of the random detuned bladed disk.

[0012] This invention also provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the multi-agent model synchronous simulation method for evaluating the probabilistic flutter of a stochastic detuned bladed disk described above.

[0013] This invention also provides a computer-readable storage medium storing an information transmission implementation program. When the program is executed by a processor, it implements the steps of the multi-agent model synchronous simulation method for evaluating the probabilistic flutter of a stochastic detuned bladed disk described above.

[0014] Using the embodiments of the present invention for probabilistic flutter assessment of random detuned bladed disks can improve the calculation accuracy and efficiency of probabilistic flutter assessment of random detuned bladed disks. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of the multi-agent model synchronous simulation method for evaluating probabilistic flutter of stochastic detuned bladed disks according to an embodiment of the present invention; Figure 2 This is a detailed flowchart of the multi-agent model synchronous simulation method for evaluating probabilistic flutter of stochastic detuned bladed disks according to an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the principle of the multi-agent model synchronous simulation method for probabilistic flutter assessment of stochastic detuned bladed disks according to an embodiment of the present invention. Figure 4 This is a schematic diagram of a multi-agent model synchronous simulation device for evaluating probabilistic flutter of a stochastic detuned bladed disk according to an embodiment of the present invention; Figure 5 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0017] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0018] Method Implementation Examples According to embodiments of the present invention, a multi-agent model synchronous simulation method for assessing probabilistic flutter of stochastic detuned bladed disks is provided. Figure 1 This is a flowchart of a multi-agent model synchronous simulation method for assessing probabilistic flutter of stochastic detuned bladed disks according to an embodiment of the present invention, as shown below. Figure 1 As shown, the multi-agent model synchronous simulation method for probabilistic flutter assessment of stochastic detuned bladed disks according to an embodiment of the present invention specifically includes: Step S101: Based on the dynamic model of the detuned bladed disk rotor, the fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain, and the input random variables of the two models are determined; a multi-channel blade cascade mesh model in the fluid domain and a finite element model of the blade in the solid domain are established, and deterministic analysis in the fluid and solid domains is performed to obtain the output response; specifically including: Based on the dynamic model of the detuned bladed disk rotor, the fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain for aerodynamic matrix calculation and a blade frequency detuning model in the solid domain for detuning matrix calculation. Material parameters, rotor inlet and outlet boundary conditions, and loads are selected as input random variables in the modal aerodynamic coefficient calculation; material parameter detuning is selected as the input random variable in the blade vibration frequency detuning calculation. A single blade is extracted from the full-ring bladed disk to establish a blade finite element model, wherein the blade finite element model uses 4-node or 10-node tetrahedral elements or 8-node or 20-node hexahedral elements. 2p+1 flow channels containing a reference blade and p adjacent blades on the suction and pressure surfaces are extracted from the full-ring blade cascade to establish a 2p+1 channel blade cascade flow channel mesh model, wherein the channel blade cascade flow channel mesh model uses body-fitted structured, unstructured, or hybrid meshes. Deterministic analysis of the fluid domain and solid domain is performed through the fluid domain multi-channel blade cascade flow channel mesh model and the solid domain blade finite element model to obtain the output response.

[0019] Step S102 involves extracting a predetermined number of input samples using Latin hypercube sampling, based on the distribution characteristics of influencing factors of modal aerodynamic coefficients and blade frequency mistuning. For these input samples, deterministic analyses of the fluid and solid domains are performed using fluid dynamics and solid dynamics simulations, respectively, to construct training and testing data for surrogate models in the fluid and solid domains. Specifically, this includes: Based on the distribution characteristics of the input random variables in the calculation of modal aerodynamic coefficients, the Latin hypercube sampling method is used to sample the material parameters, rotor inlet and outlet boundary conditions, and loads multiple times to extract a predetermined number of input samples. Based on the distribution characteristics of the input random variables in the calculation of blade vibration frequency detuning, the Latin hypercube sampling method is used to sample the material parameter detuning multiple times to extract a predetermined number of input samples.

[0020] The input samples extracted for the calculation of modal aerodynamic coefficients are imported into the multi-channel blade cascade flow channel mesh model for fluid dynamics simulation. The aerodynamic influence coefficients of the reference blade vibration on itself and each adjacent blade are obtained as intermediate vector output response. The traveling wave modal coordinate transformation is performed through Fourier transform, and the aerodynamic coefficients of each order of the traveling wave modal in the traveling wave modal coordinate system are solved as the output response of the fluid domain modal aerodynamic coefficient model. The input samples extracted for calculating the blade vibration frequency detuning are imported into the blade finite element model for solid dynamics simulation, and the vibration frequency detuning of the blade is obtained as the output response of the solid domain blade frequency detuning model. By mapping the output response to the input sample one by one, the training data and test data required for modeling the fluid domain modal aerodynamic coefficient proxy model and the solid domain blade frequency detuning proxy model are constructed respectively.

[0021] Step S103 involves constructing a modal aerodynamic coefficient model and a blade frequency mistuning model using an LM-optimized vector surrogate model and a particle swarm optimization least squares support vector regression surrogate model, respectively, based on training and testing data. Specifically, this includes: For the generated fluid domain sample dataset {(x i , y i Given | i=1,2,...S}, construct a vector surrogate model topology containing one input layer, three hidden layers, and one output layer to establish the mapping relationship between the input variable x and the multiple output response y of the modal aerodynamic coefficient model. Here, the input layer represents the vector input x = [x1, x2, ..., x...]. m The output layer represents the vector output y = [y1, y2, …, y] of the proxy model. n The hidden layer represents the non-linear mapping relationship from the input layer to the output layer, expressed by the hyperbolic tangent function Tanh(x) = (e^(x-1) / x).x -e -x ) / (e x +e -x Connecting the input layer and each hidden layer, and connecting the hidden layer and the output layer through a linear function p(x) = x, a vector proxy model as shown in Equation 1 is established, where S represents the number of fluid domain sample data, m represents the number of vector inputs, n represents the number of vector outputs, and e x and e -x Representing the exponential function: Formula 1; Among them, w l+1 b represents the connection weights between neurons in the hidden layer and the output layer. l+1 The activation threshold of the output layer neurons; a l and a l-1 These represent the outputs of neurons in the current layer and the previous layer, respectively; w l b represents the connection weights between neurons in adjacent layers. l The activation threshold of neurons in the current layer; l represents the number of the current layer; j and k represent the neuron numbers in the current and previous layers, respectively; W l-1 This represents the total number of neurons in the previous layer. The vector surrogate modeling problem is transformed into an optimization problem of finding the optimal solution ζ*: Formula 2; Formula 3; Where ζ = [w, b] is the vector of parameters to be determined, w represents the connection weights, and b represents the activation threshold; L(·) represents the cost function for model training, which is usually the regression error of the model. To ensure the generalization ability of the deep neural network regression model, a regularization term is introduced into the cost function, and ‖·‖2 represents the 2-norm function. Represents the regularization parameter; Using the LM method, the optimal parameters are searched according to Formula 4: Formula 4; Formula 5; Formula 6; Formula 7; in, H(ζ) is the gradient vector; t J(ζ) is the Hessian matrix. t Let be the Jacobian matrix; I be the identity matrix; μ>0 be the damping parameter; 0<β<1 be the dynamic attenuation rate; L(x, ζ) t L(x, ζ0) represents the current cost function value; L(x, ζ0) represents the initial cost function value; Lmin (x, ζ) represents the target precision. This represents the current vector of parameters to be determined. Substituting the optimal model parameters ζ* found into Equation 1, we obtain the output aerodynamic influence coefficient response. The vector proxy model is as follows: Formula 8; in, and It is the optimal solution for connection weights and activation thresholds in the LM-optimized vector proxy model, where N represents the total number of blades in the bladed disk rotor; Performing a Fourier transform on the output aerodynamic influence coefficient response yields the modal aerodynamic coefficient model in the fluid domain. : Formula 9; For the generated solid domain sample dataset {(Δx i , y i Construct a nonlinear regression function as shown in Equation 10, using the formula | i=1,2,...,d}, to establish the mapping relationship between the input variable Δx and the output response y of the blade frequency mistuning model: Formula 10; in, This represents the mapping function between the input variable Δx and the output response y of the blade frequency detuning model, where ω is the vector of undetermined parameters. Represents the feature space mapping function; Considering the estimation accuracy and generalization ability of the least squares support vector regression model, the nonlinear regression modeling problem is transformed into an optimization problem as shown in Equation 11: Formula 11; Where γ is the regularization parameter that controls the penalty for estimation error, and d represents the number of solid domain sample data; Introducing the kernel function ψ(Δx) i , Δx j To replace the inner product in higher-dimensional space The optimization problem in Equation 11 is transformed into the dual optimization problem in Equation 12: Formula 12; Formula 13; Wherein, ψ(Δx) i , Δx j Using a hybrid kernel function, ψ1(Δx) i , Δx j ) is the Gaussian radial basis kernel function, ψ2(Δx) i, Δx j ) represents the Morlet wavelet kernel function, and a is a weighting coefficient that controls the proportion of a single kernel in the mixed kernel; Solve the optimization problem in Equation 12 to obtain the optimal solution. and b * Establish a least squares support vector regression surrogate model as shown in Equation 14: Formula 14; Where r represents the number of input variables; The optimal hyperparameters of the model are searched using a dynamic particle swarm optimization algorithm. These hyperparameters include the regularization parameter γ, weight coefficient a, Gaussian radial basis kernel width σ1, Morlet wavelet kernel frequency coefficient ω0, and Morlet wavelet kernel scaling factor σ2. Each particle represents a potential solution of the model hyperparameters. The particle position is composed of the model hyperparameters and is evaluated by the training error of the least squares support vector regression model. During the search process, all particles update their individual positions, individual extrema, and swarm extrema by tracking the current optimal particle, and update the search for the optimal solution in the solution space according to Equation 15. Formula 15; Where i represents the i-th particle, t is the current iteration number, T is the maximum iteration number, and V i X is the current particle velocity. i It is the current particle position, P i P represents the current individual extreme value. g This represents the current group extremum, where r1 and r2 are random numbers following a uniform distribution U(0,1), w(t) is the dynamic nonlinear inertia weight, and w0 is the initial inertia weight. T Here, c1(t) represents the inertia weight at the maximum number of iterations, and c2(t) represents the dynamic nonlinear individual learning factor and the dynamic nonlinear group learning factor in the t-th iteration, respectively. 1o and c 2o These are the initial individual learning factors and the initial group learning factors, respectively, c 1T and c 2T Let be the individual learning factor and the group learning factor in the Tth iteration, respectively, and e be a fixed constant. Substituting the optimal hyperparameters of the searched model into Equation 14, we obtain the blade frequency detuning model in the solid domain as shown in Equation 16: Formula 16; In the formula, The model function representing the frequency detuning of blades in the solid domain. a represents the optimal mapping function between the input variable Δx and the output response y of the blade frequency detuning model. *The optimal weighting coefficients for the hybrid kernel function are... This represents the optimal bias coefficient. This represents the Gaussian radial basis kernel function substituted with the optimal hyperparameters. This represents the Morlet wavelet kernel function with the optimal hyperparameters substituted.

[0022] Step S104 involves performing surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model, respectively, to obtain the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain. These responses are then input into the vibration equation of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue response of the detuned bladed disk rotor system and performing probabilistic flutter assessment of the random detuned bladed disk. Specifically, this includes: Based on the distribution characteristics of the input random variables in the modal aerodynamic coefficient calculation, the Latin hypercube sampling method is used to sample material parameters, rotor inlet and outlet boundary conditions, and loads to extract a large-scale input sample. The established modal aerodynamic coefficient model is used to replace the complex fluid dynamics simulation. The extracted input sample is used to perform Monte Carlo simulation to obtain the modal aerodynamic coefficient response and its statistical characteristics in the fluid domain. Based on the distribution characteristics of the input random variables in the calculation of blade vibration frequency detuning, the Latin hypercube sampling method is used to sample the material parameter detuning and extract input samples. The established blade frequency detuning model is used to replace the complex solid dynamics simulation. The extracted large-scale input samples are used to perform Monte Carlo simulation to obtain the blade frequency detuning response and its statistical characteristics in the solid domain. Using the output responses of the modal aerodynamic coefficient model and the blade frequency detuning model as inputs to the detuned bladed disk rotor vibration equation, the multi-surrogate model coordinated detuned bladed disk rotor vibration equation is obtained as shown in Equation 17: Formula 17; Formula 18; Among them, F mn (·) represents the discrete Fourier transform function. To output the frequency detuning response of the blade. This represents the inter-blade phase angle of the nth traveling wave mode. This represents the amplitude of the nth traveling wave mode. Denotes the aerodynamic coefficients of the nth traveling wave mode. ω avg This represents the average frequency of each traveling wave mode of the harmonic bladed disk rotor. λ n The eigenvalues ​​represent the nth detuned mode. This represents the frequency of the nth traveling wave mode of the harmonic bladed disk rotor; By solving the vibration equation shown in Equation 17, the complex eigenvalues ​​of the detuned bladed disk rotor system are obtained. The real part of the eigenvalue represents the system stiffness, and the imaginary part of the eigenvalue represents the system damping. The occurrence of flutter is determined based on the imaginary part of the eigenvalue. When the imaginary part of the eigenvalue is negative, flutter will occur; otherwise, flutter will not occur. Substituting the fluid domain modal aerodynamic coefficient response and the solid domain blade vibration frequency detuning response obtained from the surrogate model simulation into Equation 17, a multi-surrogate model collaborative simulation is performed to solve the vibration equation of the detuned bladed disk rotor system, obtaining the system input random variable x = [x1, x2, …, x m The corresponding modal eigenvalues ​​λ(x) are: [λ1(x), λ2(x), …,λ N [(x)], extract the imaginary part of the feature value Im(λ(x)) = [Im(λ1(x)), Im(λ2(x)), …, Im(λ)], and extract the imaginary part of the feature value Im(λ(x)) = [Im(λ1(x)), Im(λ2(x)), …, Im(λ)]. N As the output response, the limit state function G(x) for the probability analysis of random detuned impeller mechanical chatter is obtained as shown in Equation 19: Formula 19; Among them, [Im(λ n [(x))] is the allowable minimum value of the imaginary part of the eigenvalue. According to the eigenvalue criterion of flutter, [Im(λ)] n (x))]=0; Based on the sampling simulation results and the limit state function of the random detuning turbomachinery chatter probability analysis, the reliability of turbomachinery chatter considering random detuning is calculated according to Formula 20: Formula 20; Where E(·) is the mean function; λ r [G(x)] is the safety indication function for sample points within the entire sampling domain, where G(x) > 0 indicates a safe state, and G(x) ≤ 0 indicates a flutter failure state; N r N represents the number of sample points within the security region. s This represents the total number of sample points.

[0023] The following example, taking the probabilistic flutter assessment of an aero-engine compressor bladed disk rotor under random detuning conditions, further illustrates the multi-proxy model synchronous simulation method for probabilistic flutter assessment of randomly detuned bladed disks of the present invention. The specific steps are as follows: like Figure 2 , 3 As shown in the embodiment of the present invention, the multi-agent model synchronous simulation method for probabilistic flutter assessment of stochastic detuned bladed disks includes the following steps: Step (1): Based on the dynamic model of the detuned compressor bladed disk rotor, the complex fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain, and input random variables are selected.

[0024] Step (1) includes the following sub-steps: ① Based on the dynamic model of the detuned compressor bladed disk rotor, the complex fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain for calculating the aerodynamic matrix and a blade frequency detuning model in the solid domain for calculating the detuning matrix.

[0025] ② Selecting Input Random Variables. In this embodiment, for the compressor bladed disk rotor of an aero-engine under random detuning conditions, in order to quantify the influence of uncertain factors on the aerodynamic forces of each traveling wave mode, material parameters (i.e., material density, elastic modulus, Poisson's ratio), rotor inlet and outlet boundary conditions (i.e., inlet total temperature, inlet total pressure, outlet static pressure), and load (i.e., rotational speed) are selected as input random variables in the calculation of modal aerodynamic force coefficients; in order to quantify the influence of the uncertainty of blade parameter detuning on the blade vibration frequency detuning, material parameter detuning (i.e., material density detuning, elastic modulus detuning, Poisson's ratio detuning) is selected as input random variables in the calculation of blade vibration frequency detuning.

[0026] Step (2) is to establish a multi-channel blade cascade mesh model in the fluid domain and a finite element model of the blade in the solid domain to perform deterministic analysis in the fluid domain and solid domain and obtain the output response.

[0027] Step (2) includes the following sub-steps: ① Extract a single blade from the compressor's full-ring bladed disk and establish a finite element model of the blade. The finite element model uses 20-node hexahedral elements.

[0028] ② Extract nine flow channels from the compressor's full annular cascade, including a reference blade and four adjacent blades for each of the suction and pressure surfaces, and establish a nine-channel cascade flow channel mesh model. The mesh model adopts a body-fitted structured mesh.

[0029] In step (3), a small number of input samples are extracted by Latin hypercube sampling based on the distribution characteristics of the influencing factors of modal aerodynamic coefficients and blade frequency detuning.

[0030] Step (3) includes the following sub-steps: ① Based on the distribution characteristics of the input random variables in the modal aerodynamic coefficient calculation, the Latin hypercube sampling method is used to sample the material parameters (i.e., material density, elastic modulus, Poisson's ratio), rotor inlet and outlet boundary conditions (i.e., inlet total temperature, inlet total pressure, outlet static pressure) and load (i.e., speed) multiple times to extract a small number of input samples.

[0031] ② Based on the distribution characteristics of the input random variables in the calculation of blade vibration frequency detuning, the Latin hypercube sampling method is used to sample the material parameter detuning (i.e., material density detuning, elastic modulus detuning, Poisson's ratio detuning, etc.) multiple times to extract a small number of input samples.

[0032] Step (4) involves performing deterministic analysis of the fluid domain and solid domain using fluid dynamics simulation and solid dynamics simulation, respectively, to construct training and testing data for the proxy model of the fluid domain and solid domain.

[0033] Step (4) includes the following sub-steps: ① The input samples extracted for the calculation of modal aerodynamic coefficients are imported into the 9-channel blade cascade flow channel mesh model for fluid dynamics simulation. The aerodynamic influence coefficients of the reference blade vibration on itself and each adjacent blade are obtained as intermediate vector output response. The traveling wave modal coordinate transformation is performed through Fourier transform to solve the aerodynamic coefficients of each order of the traveling wave modal in the traveling wave modal coordinate system as the output response of the fluid domain modal aerodynamic coefficient model.

[0034] ② The input samples extracted for calculating the blade vibration frequency detuning are imported into the blade finite element model for solid dynamics simulation, and the vibration frequency detuning of the blade is obtained as the output response of the solid domain blade frequency detuning model.

[0035] ③ Correspond the output response to the input samples one by one, and construct the training and test samples required for modeling the fluid domain modal aerodynamic coefficient proxy model and the solid domain blade frequency detuning proxy model, respectively.

[0036] Step (5) uses the LM-optimized vector surrogate model and the particle swarm optimization least squares support vector regression surrogate model to construct the modal aerodynamic coefficient model and the blade frequency detuning model respectively through training and test samples.

[0037] ① For the generated fluid domain sample dataset {(xi, yi)| i=1,2,...,s}, a vector surrogate model topology containing one input layer, three hidden layers, and one output layer is constructed to establish the mapping relationship between the input variable x and the multiple output response y of the modal aerodynamic coefficient model. Here, the input layer represents the vector input x = [x1,x2, …, xm] of the surrogate model, the output layer represents the vector output y = [y1, y2, …, yn] of the surrogate model, and the hidden layers represent the nonlinear mapping relationship from the input layer to the output layer. By connecting the input layer and each hidden layer using the hyperbolic tangent function Tanh(x)=(ex-ex) / (ex+ex), and by connecting the hidden layer and the output layer using the linear function p(x)=x, the following vector surrogate model can be established. (1) In the formula, wl+1 is the connection weight between neurons in the hidden layer and the output layer; bl+1 is the activation threshold of neurons in the output layer; al and al-1 represent the outputs of neurons in the current layer and the previous layer, respectively; wl is the connection weight between neurons in adjacent layers; bl is the activation threshold of neurons in the current layer; l represents the number of the current layer; j and k represent the number of neurons in the current layer and the previous layer, respectively; Wl-1 is the total number of neurons in the previous layer.

[0038] ② The modeling problem of the vector surrogate model is transformed into an optimization problem of finding the optimal solution ζ*: (2) In the formula, ζ = [w, b] is the vector of parameters to be determined; L(·) represents the cost function for model training, which is usually the regression error of the model. To ensure the generalization ability of the deep neural network regression model, a regularization term is introduced into the cost function. (3) Where, ‖·‖2 represents the 2-norm function.

[0039] ③ Using the Levenberg–Marquardt (LM) method, search for the optimal parameters according to the following update formula. (4) In the formula, H(ζt) is the gradient vector; H(ζt) is the Hessian matrix, which is approximately expressed as follows: (5) In the formula, J(ζt) is the Jacobian matrix; I is the identity matrix; μ>0 is the damping parameter, and its update formula is as follows: (6) In the formula, 0 < β < 1 represents the dynamic decay rate, which varies with the distance between the cost function value and the target accuracy according to the following formula. (7) In the formula, L(x, ζt) is the current cost function value; L(x, ζ0) is the initial cost function value; and Lmin(x, ζ) is the target accuracy.

[0040] ④ Substitute the optimal model parameter ζ* found into equation (1) to obtain the output aerodynamic influence coefficient response. The vector proxy model is (8) In the formula, and It is the optimal solution for connection weights and activation thresholds in the LM-optimized vector proxy model.

[0041] Performing a Fourier transform on the output aerodynamic influence coefficient response yields the modal aerodynamic coefficient model for the fluid domain as follows: (9) ⑤ For the generated solid domain sample dataset {(Δxi, yi)| i=1,2,...,d}, construct the following nonlinear regression function to establish the mapping relationship between the input variable Δx and the output response y of the blade frequency detuning model.

[0042] (10) In the formula, ω is the vector of parameters to be determined.

[0043] ⑥ Considering the estimation accuracy and generalization ability of the least squares support vector regression model, the nonlinear regression modeling problem is transformed into the following optimization problem: (11) In the formula, γ is a regularization parameter that controls the penalty for estimation error.

[0044] We introduce a kernel function ψ(Δxi, Δxj) to replace the inner product in high-dimensional space. The optimization problem in equation (11) is transformed into the following dual optimization problem. (12) In the formula, ψ(Δxi, Δxj) adopts a hybrid kernel function. (13) In the formula, ψ1(Δxi, Δxj) is the Gaussian radial basis kernel function, ψ2(Δxi, Δxj) is the Morlet wavelet kernel function, and a is the weighting coefficient that controls the proportion of a single kernel in the mixed kernel.

[0045] ⑦ Solve the optimization problem in equation (12) to obtain the optimal solutions βi* and b*, and then establish the following least squares support vector regression surrogate model. (14) ⑧ The optimal hyperparameters of the model (including regularization parameter γ, weight coefficient a, Gaussian radial basis kernel width σ1, Morlet wavelet kernel frequency coefficient ω0, and Morlet wavelet kernel scaling factor σ2) are searched using a dynamic particle swarm optimization algorithm. Each particle represents a potential solution of the model hyperparameters, and the particle position is composed of the model hyperparameters and evaluated by the training error of the least squares support vector regression model. During the search process, all particles search for the optimal solution in the solution space by tracking the current best particle and updating the individual position, individual extremum, and swarm extremum of the particles according to the following update formula. (15) In the formula, i represents the i-th particle, t is the current iteration number, T is the maximum iteration number, Vi is the current particle velocity, Xi is the current particle position, Pi represents the current individual extreme value, Pg represents the current group extreme value, r1 and r2 are random numbers following a uniform distribution U(0, 1), w(t) is the dynamic nonlinear inertia weight, w0 is the initial inertia weight, wT is the inertia weight at the maximum iteration number, c1(t) and c2(t) are the dynamic nonlinear individual learning factor and dynamic nonlinear group learning factor in the t-th iteration, respectively, c1o and c2o are the initial individual learning factor and initial group learning factor, respectively, c1T and c2T are the individual learning factor and group learning factor in the T-th iteration, respectively, and e is a fixed constant.

[0046] ⑨ Substituting the optimal hyperparameters of the searched model into equation (14), the blade frequency detuning model in the solid domain can be obtained as follows: (16) In the formula, a* is the optimal weight coefficient of the hybrid kernel function, ψ1*(Δxi, Δx) represents the Gaussian radial basis kernel function with the optimal hyperparameters, and ψ2*(Δxi, Δx) represents the Morlet wavelet kernel function with the optimal hyperparameters.

[0047] Step (6) involves performing surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model to obtain the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain.

[0048] Step (6) includes the following sub-steps: ① Based on the distribution characteristics of the input random variables in the modal aerodynamic coefficient calculation, the Latin hypercube sampling method is used to sample the material parameters (i.e., material density, elastic modulus, Poisson's ratio), rotor inlet and outlet boundary conditions (i.e., inlet total temperature, inlet total pressure, outlet static pressure) and load (i.e., rotational speed), and 10,000 sets of input samples are drawn.

[0049] ② The established modal aerodynamic coefficient model is used to replace the complex fluid dynamics simulation. 10,000 sets of input samples are input to perform Monte Carlo simulation to obtain the modal aerodynamic coefficient response and its statistical characteristics in the fluid domain (scatter density cloud map of traveling wave mode root locus, distribution histogram of minimum imaginary part of modal aerodynamic coefficient, etc.).

[0050] ③ Based on the distribution characteristics of the input random variables in the calculation of blade vibration frequency detuning, the Latin hypercube sampling method is used to sample the material parameter detuning (i.e., material density detuning, elastic modulus detuning, and Poisson's ratio detuning), and 10,000 sets of input samples are drawn.

[0051] ④ Use the established blade frequency detuning model to replace the complex solid dynamics simulation. Input 10,000 sets of sampled data to perform Monte Carlo simulation and obtain the blade frequency detuning response and its statistical characteristics (distribution histogram, distribution mean, standard deviation, etc.) in the solid domain.

[0052] Step (7) inputs the modal aerodynamic coefficient response and blade frequency detuning response into the detuned compressor bladed disk rotor vibration equation for co-simulation and solution, thereby obtaining the characteristic value response of the detuned compressor bladed disk rotor system and performing probabilistic flutter assessment of the random detuned compressor bladed disk.

[0053] Step (7) includes the following sub-steps: ① By using the output responses of the modal aerodynamic coefficient model and the blade frequency detuning model as inputs to the vibration equation of the detuned compressor bladed disk rotor, the vibration equation of the detuned compressor bladed disk rotor obtained by multi-surrogate model coordination can be obtained as follows: (17) in, (18) In the formula, Fmn(·) is the discrete Fourier transform function. This is the output blade frequency detuning response.

[0054] By solving this vibration equation, the complex eigenvalues ​​of the detuned compressor bladed disk rotor system can be obtained. The real part of the eigenvalues ​​characterizes the system stiffness, and the imaginary part characterizes the system damping. The imaginary part of the eigenvalues ​​can be used to determine whether flutter has occurred; when the imaginary part is negative, flutter will occur, and vice versa.

[0055] ② Substitute the fluid domain modal aerodynamic coefficient response and the solid domain blade vibration frequency detuning response obtained from 10,000 sets of surrogate model simulations into equation (17) for multi-surrogate model collaborative simulation, solve the vibration equation of the detuned compressor bladed disk rotor system, and thus obtain the modal eigenvalues ​​λ(x) = [λ1(x), λ2(x), …, λN(x)] corresponding to the system input random variable x = [x1, x2, …, xm]. Extract the imaginary part Im(λ(x)) = [Im(λ1(x)), Im(λ2(x)), …, Im(λN(x))] of the eigenvalues ​​as the output response, and then obtain the limit state function of the probability analysis of random detuned compressor bladed disk flutter as follows: (19) In the formula, [Im(λn(x))] is the allowable minimum value of the imaginary part of the eigenvalue. According to the eigenvalue criterion of flutter, [Im(λn(x))]=0.

[0056] ③ Based on 10,000 sets of simulation results and the limit state function of random detuning compressor disk flutter probability analysis, the reliability of compressor disk flutter considering random detuning can be calculated according to the following formula. (20) In the formula, E(·) is the mean function; λr[G(x)] is the safety indication function of the sample points in the entire sampling domain, where G(x)>0 indicates a safe state and G(x)≤0 indicates a flutter failure state; Nr is the number of sample points in the safe domain and Ns is the total number of sample points.

[0057] The beneficial effects of the technical solution in the embodiments of the present invention are as follows: In terms of computational efficiency: the multi-surrogate model synchronous simulation method uses an LM-optimized vector surrogate model and a particle swarm optimization least squares support vector regression surrogate model to replace complex fluid dynamics and solid dynamics calculations, thereby avoiding a large number of numerical simulation calculations and significantly improving computational efficiency. In terms of computational accuracy: (1) The multi-surrogate model synchronous simulation method decomposes the fluid-structure interaction system into fluid domain and solid domain and performs surrogate model modeling separately, thereby reducing the nonlinearity and complexity of surrogate model modeling, avoiding the overfitting problem in direct surrogate model modeling, and ensuring the prediction accuracy of the surrogate model for the fluid domain and solid domain response; (2) The multi-surrogate model synchronous simulation method uses the detuned bladed disk rotor vibration equation to coordinate the surrogate models of fluid domain and solid domain, which can better reflect the coupling interaction between fluid domain and solid domain, thereby ensuring the accuracy of the detuned bladed disk rotor vibration response prediction.

[0058] Device Example 1 According to embodiments of the present invention, a multi-agent model synchronous simulation device for assessing probabilistic flutter of stochastic detuned bladed disks is provided. Figure 4 This is a schematic diagram of a multi-agent model synchronous simulation device for evaluating probabilistic flutter of stochastic detuned bladed disks according to an embodiment of the present invention, as shown below. Figure 4 As shown, the multi-agent model synchronous simulation device for probabilistic flutter assessment of stochastic detuned bladed disks according to an embodiment of the present invention specifically includes: The decomposition analysis module 40 is used to decompose the fluid-structure interaction vibration model into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain based on the dynamic model of the detuned bladed disk rotor, and to determine the input random variables of the two models; to establish a multi-channel blade cascade mesh model in the fluid domain and a blade finite element model in the solid domain, to perform deterministic analysis in the fluid domain and solid domain, and to obtain the output response; The extraction and analysis module 42 is used to extract a predetermined number of input samples based on the distribution characteristics of the influencing factors of modal aerodynamic coefficients and blade frequency mistuning, respectively, through Latin hypercube sampling; for the input samples, deterministic analysis of the fluid domain and solid domain is completed through fluid dynamics simulation and solid dynamics simulation, respectively, and training data and test data for modeling proxy models of the fluid domain and solid domain are constructed. Module 44 is used to construct modal aerodynamic coefficient models and blade frequency mistuning models using LM-optimized vector surrogate models and particle swarm optimization least squares support vector regression surrogate models, respectively, through training and testing data. The simulation solution module 46 is used to perform surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model, respectively, to obtain the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain. The modal aerodynamic coefficient response and the blade frequency detuning response are then input into the vibration equation of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue response of the detuned bladed disk rotor system and performing probabilistic flutter assessment of the random detuned bladed disk.

[0059] The embodiments of the present invention are device embodiments corresponding to the above method embodiments. The specific operation of each module can be understood with reference to the description of the method embodiments, and will not be repeated here.

[0060] Device Example 2 This invention provides an electronic device, such as... Figure 5 As shown, it includes: a memory 50, a processor 52, and a computer program stored in the memory 50 and executable on the processor 52, wherein the computer program, when executed by the processor 52, performs the steps as described in the method embodiment.

[0061] Device Example 3 This invention provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor 52, performs the steps described in the method embodiment.

[0062] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.

[0063] 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 present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-agent model synchronous simulation method for assessing probabilistic flutter of stochastic detuned bladed disks, characterized in that, include: Based on the dynamic model of the detuned bladed disk rotor, the fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain, and the input random variables of the two models are determined. A multi-channel blade cascade mesh model in the fluid domain and a blade finite element model in the solid domain are established to perform deterministic analysis in the fluid domain and solid domain and obtain the output response. Based on the distribution characteristics of the influencing factors of modal aerodynamic coefficients and blade frequency mistuning, a predetermined number of input samples are extracted by Latin hypercube sampling. For the input samples, deterministic analysis of the fluid domain and solid domain is completed by fluid dynamics simulation and solid dynamics simulation, respectively, and training data and test data for surrogate modeling of fluid domain and solid domain are constructed. Using the LM-optimized vector surrogate model and the particle swarm optimization least squares support vector regression surrogate model, modal aerodynamic coefficient model and blade frequency detuning model are constructed respectively using training data and test data; By performing surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model respectively, the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain are obtained. The modal aerodynamic coefficient response and the blade frequency detuning response are then input into the vibration equation of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue response of the detuned bladed disk rotor system and performing probabilistic flutter assessment of the random detuned bladed disk.

2. The method according to claim 1, characterized in that, Based on the dynamic model of the detuned bladed disk rotor, the fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain. The specific input random variables of the two models are determined as follows: Based on the dynamic model of the detuned bladed disk rotor, the fluid-structure interaction vibration model is decomposed into a modal aerodynamic coefficient model in the fluid domain for calculating the aerodynamic matrix and a blade frequency detuning model in the solid domain for calculating the detuning matrix. Material parameters, rotor inlet and outlet boundary conditions, and loads are selected as input random variables in the modal aerodynamic coefficient calculation; material parameter detuning is selected as the input random variable in the blade vibration frequency detuning calculation.

3. The method according to claim 2, characterized in that, Establish a mesh model of the multi-channel cascade flow channel in the fluid domain and a finite element model of the blade in the solid domain, perform deterministic analysis in both the fluid and solid domains, and obtain the output response, specifically including: A single blade is extracted from the full-ring bladed disk to establish a finite element model of the blade, wherein the finite element model of the blade adopts 4-node or 10-node tetrahedral elements or 8-node or 20-node hexahedral elements; 2p+1 flow channels containing a reference blade and p adjacent blades of suction and pressure surfaces are extracted from the full-ring bladed disk to establish a 2p+1 channel bladed disk flow channel mesh model, wherein the channel bladed disk flow channel mesh model adopts body-fitted structured, unstructured or hybrid mesh; Deterministic analysis of the fluid and solid domains was performed using a multi-channel blade cascade mesh model in the fluid domain and a finite element model of the blade in the solid domain to obtain the output response.

4. The method according to claim 1, characterized in that, Based on the distribution characteristics of influencing factors of modal aerodynamic coefficients and blade frequency mistuning, a predetermined number of input samples are extracted using Latin hypercube sampling, specifically including: Based on the distribution characteristics of the input random variables in the calculation of modal aerodynamic coefficients, the Latin hypercube sampling method is used to sample the material parameters, rotor inlet and outlet boundary conditions, and loads multiple times to extract a predetermined number of input samples. Based on the distribution characteristics of the input random variables in the calculation of blade vibration frequency detuning, the Latin hypercube sampling method is used to sample the material parameter detuning multiple times to extract a predetermined number of input samples.

5. The method according to claim 1, characterized in that, For the input samples, deterministic analyses of the fluid and solid domains are performed using fluid dynamics and solid dynamics simulations, respectively. The training and testing data for constructing the surrogate models in the fluid and solid domains specifically include: The input samples extracted for the calculation of modal aerodynamic coefficients are imported into the multi-channel blade cascade flow channel mesh model for fluid dynamics simulation. The aerodynamic influence coefficients of the reference blade vibration on itself and each adjacent blade are obtained as intermediate vector output response. The traveling wave modal coordinate transformation is performed through Fourier transform, and the aerodynamic coefficients of each order of the traveling wave modal in the traveling wave modal coordinate system are solved as the output response of the fluid domain modal aerodynamic coefficient model. The input samples extracted for calculating the blade vibration frequency detuning are imported into the blade finite element model for solid dynamics simulation, and the vibration frequency detuning of the blade is obtained as the output response of the solid domain blade frequency detuning model. By mapping the output response to the input sample one by one, the training data and test data required for modeling the fluid domain modal aerodynamic coefficient proxy model and the solid domain blade frequency detuning proxy model are constructed respectively.

6. The method according to claim 1, characterized in that, Using an LM-optimized vector surrogate model and a particle swarm optimization least squares support vector regression surrogate model, modal aerodynamic coefficient models and blade frequency mistuning models are constructed using training and testing data, respectively, including: For the generated fluid domain sample dataset {(x i , y i Given | i=1,2,...S}, construct a vector surrogate model topology containing one input layer, three hidden layers, and one output layer to establish the mapping relationship between the input variable x and the multiple output response y of the modal aerodynamic coefficient model. Here, the input layer represents the vector input x = [x1, x2, …, x…]. m The output layer represents the vector output y = [y1, y2, …, y] of the proxy model. n The hidden layer represents the non-linear mapping relationship from the input layer to the output layer, expressed by the hyperbolic tangent function Tanh(x) = (e^(x-1) / x). x -e -x ) / (e x +e -x Connecting the input layer and each hidden layer, and connecting the hidden layer and the output layer through a linear function p(x) = x, a vector proxy model as shown in Equation 1 is established, where S represents the number of fluid domain sample data, m represents the number of vector inputs, n represents the number of vector outputs, and e x and e -x Representing the exponential function: Formula 1; Among them, w l+1 b represents the connection weights between neurons in the hidden layer and the output layer. l+1 The activation threshold of the output layer neurons; a l and a l-1 These represent the outputs of neurons in the current layer and the previous layer, respectively; w l b represents the connection weights between neurons in adjacent layers. l The activation threshold of neurons in the current layer; l represents the number of the current layer; j and k represent the neuron numbers in the current and previous layers, respectively; W l-1 This represents the total number of neurons in the previous layer. The vector surrogate modeling problem is transformed into an optimization problem of finding the optimal solution ζ*: Official 2; Official 3; Where ζ = [w, b] is the vector of parameters to be determined, w represents the connection weights, and b represents the activation threshold; L(·) represents the cost function for model training, which is usually the regression error of the model. To ensure the generalization ability of the deep neural network regression model, a regularization term is introduced into the cost function, and ‖·‖2 represents the 2-norm function. Represents the regularization parameter; Using the LM method, the optimal parameters are searched according to Formula 4: Official 4; Official 5; Official 6; Official 7; in, H(ζ) is the gradient vector; t J(ζ) is the Hessian matrix. t Let be the Jacobian matrix; I be the identity matrix; μ>0 be the damping parameter; 0<β<1 be the dynamic attenuation rate; L(x, ζ) t L(x, ζ0) represents the current cost function value; L(x, ζ0) represents the initial cost function value; L min (x, ζ) represents the target precision. This represents the current vector of parameters to be determined. Substituting the optimal model parameters ζ* found into Equation 1, we obtain the output aerodynamic influence coefficient response. The vector proxy model is as follows: Official 8; in, and It is the optimal solution for connection weights and activation thresholds in the LM-optimized vector proxy model, where N represents the total number of blades in the bladed disk rotor; Performing a Fourier transform on the output aerodynamic influence coefficient response yields the modal aerodynamic coefficient model in the fluid domain. : Official 9; For the generated solid domain sample dataset {(Δx i , y i Construct a nonlinear regression function as shown in Equation 10, using the formula | i=1,2,...,d}, to establish the mapping relationship between the input variable Δx and the output response y of the blade frequency mistuning model: Official 10; in, This represents the mapping function between the input variable Δx and the output response y of the blade frequency detuning model, where ω is the vector of undetermined parameters. Represents the feature space mapping function; Considering the estimation accuracy and generalization ability of the least squares support vector regression model, the nonlinear regression modeling problem is transformed into an optimization problem as shown in Equation 11: Official 11; Where γ is the regularization parameter that controls the penalty for estimation error, and d represents the number of solid domain sample data; Introducing the kernel function ψ(Δx) i , Δx j To replace the inner product in higher-dimensional space The optimization problem in Equation 11 is transformed into the dual optimization problem in Equation 12: Official 12; Official 13; Wherein, ψ(Δx) i , Δx j Using a hybrid kernel function, ψ1(Δx) i , Δx j ) is the Gaussian radial basis kernel function, ψ2(Δx) i ,Δx j ) represents the Morlet wavelet kernel function, and a is a weighting coefficient that controls the proportion of a single kernel in the mixed kernel; Solve the optimization problem in Equation 12 to obtain the optimal solution. and b * Establish a least squares support vector regression surrogate model as shown in Equation 14: Official 14; Where r represents the number of input variables; The optimal hyperparameters of the model are searched using a dynamic particle swarm optimization algorithm. These hyperparameters include the regularization parameter γ, weight coefficient a, Gaussian radial basis kernel width σ1, Morlet wavelet kernel frequency coefficient ω0, and Morlet wavelet kernel scaling factor σ2. Each particle represents a potential solution of the model hyperparameters. The particle position is composed of the model hyperparameters and is evaluated by the training error of the least squares support vector regression model. During the search process, all particles update their individual positions, individual extrema, and swarm extrema by tracking the current optimal particle, and update the search for the optimal solution in the solution space according to Equation 15. Official 15; Where i represents the i-th particle, t is the current iteration number, T is the maximum iteration number, and V i X is the current particle velocity. i It is the current particle position, P i P represents the current individual extreme value. g Let r1 and r2 be random numbers following a uniform distribution U(0, 1), and w(t) be the dynamic nonlinear inertia weight, with w0 being the initial inertia weight. T Here, c1(t) represents the inertia weight at the maximum number of iterations, and c2(t) represents the dynamic nonlinear individual learning factor and the dynamic nonlinear group learning factor in the t-th iteration, respectively. 1o and c 2o These are the initial individual learning factors and the initial group learning factors, respectively, c 1T and c 2T Let be the individual learning factor and the group learning factor in the Tth iteration, respectively, and e be a fixed constant. Substituting the optimal hyperparameters of the searched model into Equation 14, we obtain the blade frequency detuning model in the solid domain as shown in Equation 16: Official 16; In the formula, The model function representing the frequency detuning of blades in the solid domain. a represents the optimal mapping function between the input variable Δx and the output response y of the blade frequency detuning model. * The optimal weighting coefficients for the hybrid kernel function are... This represents the optimal bias coefficient. This represents the Gaussian radial basis kernel function substituted with the optimal hyperparameters. This represents the Morlet wavelet kernel function with the optimal hyperparameters substituted.

7. The method according to claim 1, characterized in that, Surrogate model simulations are performed based on modal aerodynamic coefficient models and blade frequency detuning models to obtain the modal aerodynamic coefficient responses in the fluid domain and the blade frequency detuning responses in the solid domain. These modal aerodynamic coefficient responses and blade frequency detuning responses are then input into the vibration equations of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue responses of the detuned bladed disk rotor system. The specific steps for evaluating the probabilistic flutter of the stochastic detuned bladed disk include: Based on the distribution characteristics of the input random variables in the modal aerodynamic coefficient calculation, the Latin hypercube sampling method is used to sample material parameters, rotor inlet and outlet boundary conditions, and loads to extract a large-scale input sample. The established modal aerodynamic coefficient model is used to replace the complex fluid dynamics simulation. The extracted input sample is used to perform Monte Carlo simulation to obtain the modal aerodynamic coefficient response and its statistical characteristics in the fluid domain. Based on the distribution characteristics of the input random variables in the calculation of blade vibration frequency detuning, the Latin hypercube sampling method is used to sample the material parameter detuning and extract input samples. The established blade frequency detuning model is used to replace the complex solid dynamics simulation. The extracted large-scale input samples are used to perform Monte Carlo simulation to obtain the blade frequency detuning response and its statistical characteristics in the solid domain. Using the output responses of the modal aerodynamic coefficient model and the blade frequency detuning model as inputs to the detuned bladed disk rotor vibration equation, the multi-surrogate model coordinated detuned bladed disk rotor vibration equation is obtained as shown in Equation 17: Official 17; Official 18; Among them, F mn (·) represents the discrete Fourier transform function. To output the frequency detuning response of the blade. This represents the inter-blade phase angle of the nth traveling wave mode. This represents the amplitude of the nth traveling wave mode. Denotes the aerodynamic coefficients of the nth traveling wave mode. ω avg This represents the average frequency of each traveling wave mode of the harmonic bladed disk rotor. λ n The eigenvalues ​​represent the nth detuned mode. This represents the frequency of the nth traveling wave mode of the harmonic bladed disk rotor; By solving the vibration equation shown in Equation 17, the complex eigenvalues ​​of the detuned bladed disk rotor system are obtained. The real part of the eigenvalue represents the system stiffness, and the imaginary part of the eigenvalue represents the system damping. The occurrence of flutter is determined based on the imaginary part of the eigenvalue. When the imaginary part of the eigenvalue is negative, flutter will occur; otherwise, flutter will not occur. Substituting the fluid domain modal aerodynamic coefficient response and the solid domain blade vibration frequency detuning response obtained from the surrogate model simulation into Equation 17, a multi-surrogate model collaborative simulation is performed to solve the vibration equation of the detuned bladed disk rotor system, obtaining the system input random variable x = [x1, x2, …, x m The corresponding modal eigenvalues ​​λ(x) are: [λ1(x), λ2(x), …, λ N [(x)], extract the imaginary part of the feature value Im(λ(x)) = [Im(λ1(x)), Im(λ2(x)), …, Im(λ)], and extract the imaginary part of the feature value Im(λ(x)) = [Im(λ1(x)), Im(λ2(x)), …, Im(λ)]. N As the output response, the limit state function G(x) for the probability analysis of random detuned impeller mechanical chatter is obtained as shown in Equation 19: Official 19; Among them, [Im(λ n [(x))] is the allowable minimum value of the imaginary part of the eigenvalue. According to the eigenvalue criterion of flutter, [Im(λ)] n (x))]=0; Based on the sampling simulation results and the limit state function of the random detuning turbomachinery chatter probability analysis, the reliability of turbomachinery chatter considering random detuning is calculated according to Formula 20: Official 20; Where E(·) is the mean function; λ r [G(x)] is the safety indication function for sample points within the entire sampling domain, where G(x) > 0 indicates a safe state, and G(x) ≤ 0 indicates a flutter failure state; N r N represents the number of sample points within the security region. s This represents the total number of sample points.

8. A multi-agent model synchronous simulation device for assessing probabilistic flutter of stochastic detuned bladed disks, characterized in that, include: The decomposition analysis module is used to decompose the fluid-structure interaction vibration model into a modal aerodynamic coefficient model in the fluid domain and a blade frequency detuning model in the solid domain based on the dynamic model of the detuned bladed disk rotor, and to determine the input random variables of the two models; to establish a multi-channel blade cascade mesh model in the fluid domain and a finite element model of the blade in the solid domain, to perform deterministic analysis in the fluid domain and solid domain, and to obtain the output response; The extraction and analysis module is used to extract a predetermined number of input samples based on the distribution characteristics of the influencing factors of modal aerodynamic coefficients and blade frequency mistuning, respectively, through Latin hypercube sampling; for the input samples, deterministic analysis of the fluid domain and solid domain is completed through fluid dynamics simulation and solid dynamics simulation, respectively, and training data and test data for modeling proxy models of the fluid domain and solid domain are constructed. The module is used to construct modal aerodynamic coefficient models and blade frequency mistuning models using LM-optimized vector surrogate models and particle swarm optimization least squares support vector regression surrogate models, respectively, through training and testing data. The simulation solution module is used to perform surrogate model simulations based on the modal aerodynamic coefficient model and the blade frequency detuning model, respectively, to obtain the modal aerodynamic coefficient response in the fluid domain and the blade frequency detuning response in the solid domain. The modal aerodynamic coefficient response and the blade frequency detuning response are then input into the vibration equation of the detuned bladed disk rotor for co-simulation and solution, thereby obtaining the eigenvalue response of the detuned bladed disk rotor system and performing probabilistic flutter assessment of the random detuned bladed disk.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the multi-agent model synchronous simulation method for assessing probabilistic flutter of a stochastic detuned bladed disk as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an implementation program for information transmission, which, when executed by a processor, implements the steps of the multi-agent model synchronous simulation method for probabilistic flutter assessment of stochastic detuned bladed disks as described in any one of claims 1 to 7.

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