CN116305564A - Design method of digital twin model test bed of aero-engine rotor system - Google Patents
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Abstract
The invention provides a design method of a digital twin model test bed of an aero-engine rotor system, which comprises the following steps: constructing a numerical model, calculating rotor dynamics characteristics and acquiring rotor dynamics data; constructing an artificial intelligent model, inputting the rotor dynamics data acquired by the numerical model into the artificial intelligent model, and carrying out training prediction on the artificial intelligent model; and constructing an updating model, and updating and correcting the data of the rotor test bed in the running process through the updating model and the real-time test data. According to the technical scheme, real-time mapping of the rotor test bed entity and the digital twin model is realized, and the vibration characteristics of a rotor system are truly reflected. The method adopts a numerical model and an artificial intelligent model as data driving of a digital twin model to solve the problem of real-time mapping of a rotor test bed; the rotor test bed data is updated and corrected in the running process by updating the model and the real-time test data, so that the problem that errors of the real model and the digital twin model become larger gradually along with time is solved.
Description
Technical Field
The invention relates to the technical field of digital twin, in particular to a design method of a digital twin model test bed of an aero-engine rotor system.
Background
In the testing and testing stage of the digital twin full life cycle of the rotor test bed, the rotor test has great limitation due to the complex structure, long development period and great testing risk of the rotor. Therefore, aiming at the problems, the digital twin system is utilized to perform virtual-real mapping on the rotor test bed to form an effective way, so that the vibration characteristics of the rotor system can be truly reflected, the test risk is reduced, and the influence mechanism is revealed.
The digital twin technology can realize information interaction between a physical system and a digital twin virtual space, and can integrate various data analysis, complex feature extraction and other intelligent computing methods, so that the method is suitable for solving the problems of virtual-real mapping and state monitoring analysis of complex industrial equipment such as a rotor system. The existing digital twin modeling method of the rotor system mostly adopts a finite element method (FE), computational Fluid Dynamics (CFD), multidisciplinary mechanism analysis and deep learning combination method, and as the difference exists between the system simulation and the test measurement result, the error gradually increases along with the time, and finally the physical model cannot be truly fitted. Therefore, the model design by updating the established digital twin model has important scientific and practical significance.
The related patents total four: the invention discloses a digital twin modeling method of a turbine disc-rotor-supporting system of an aeroengine, which establishes a multi-physical-field simulation platform combined by a plurality of sub-models, and optimizes the unified physical model by establishing the unified physical model and comparing and analyzing the simulation calculation result with measured signals after noise reduction feature extraction processing, thereby obtaining the digital twin model of the turbine disc-rotor-supporting system of the aeroengine in real time. The invention discloses a method for predicting the residual life of a turbine disk of a digital twin-driven aeroengine, which is disclosed in the patent of a method for predicting the residual life of the turbine disk of the digital twin-driven aeroengine, wherein digital twin of the turbine disk of the aeroengine is utilized to simulate a vibration signal of the turbine disk, and finally, an updated damage model of the turbine disk of the aeroengine is utilized to calculate the residual life. The invention discloses a digital twin modeling method of a bearing test bed, which utilizes a finite element model and deep learning to combine to construct a digital twin model, realizes the simulation analysis of complex working conditions of the bearing test bed in a lubrication state, and can acquire operation parameters with high reliability in real time. The invention discloses a test bed system based on digital twin, which comprises a physical test bed system, a virtual test bed system and an integrated service system, wherein the information flow between the service systems is utilized to mutually transmit, and the dynamic process of collision vibration of blades is efficiently and fully researched.
Although the above-mentioned digital twin modeling method of the rotor system provides some modeling schemes, some problems still exist, and specific technical characteristics and defect analysis are as follows:
although the digital twin modeling method of the turbine disc-rotor-supporting system of the aeroengine is provided in the patent of the invention, only the structural dynamics model, the thermodynamic coupling model, the stress analysis model and the damage evolution model are considered, the established digital twin model is not updated and corrected, so that errors of the real model and the digital twin model become larger gradually along with time, and the mapping precision of the digital twin model and a physical entity is seriously influenced, and a specific scheme for solving the problem is not provided in the patent.
The digital twin model established in the digital twin-driven method for predicting the residual life of the turbine disk of the aeroengine comprises a rotor system, a bearing is worn, the oil film temperature is too high or the vibration of the rotor is unstable, working conditions/environment parameters are input into a unified physical model in real time, the unified physical model is utilized to carry out simulation calculation on real-time vibration signals of the turbine disk of the aeroengine, although the authenticity of the digital twin model is ensured, a time step is not considered, the digital twin model can have the authenticity before the operation, but the data precision cannot be ensured in the operation process, and a specific scheme for solving the problem is not given in the patent.
The invention discloses a digital twin modeling method of a bearing test bed based on effective fusion of data driving and a physical model, which is established in the patent of the invention, and is used for collecting signals such as vibration, rotation speed, temperature and the like of the bearing test bed in real time, testing the accuracy of a proxy model based on the proxy model and utilizing online data, but the correction of the patent is only aimed at the test of the proxy model, and the actually used digital twin model is not updated and corrected.
The online simulation analysis of the digital twin test bed system constructed in the digital twin test bed system cannot meet the real-time requirement and cannot update the model on the basis of the real-time requirement.
The above problems can be known that the existing digital twin modeling method does not provide a specific scheme for ensuring the updating of the digital twin model, the twin model is complex, the real-time interaction between the digital twin model and a physical entity is difficult to realize, and the accuracy of the digital twin is seriously affected.
Disclosure of Invention
According to the technical problem, a digital twin model test bed for an aero-engine rotor system is provided. The invention aims to establish a digital twin model for guaranteeing real-time mapping of vibration characteristics of a rotor test bed, realize real-time mapping of a rotor test bed entity and the digital twin model, truly reflect the vibration characteristics of a rotor system, reduce test risks and reveal influence mechanisms. Aiming at the physical structure of a rotor test bed, a digital twin model modeling mode based on the combination of a numerical model, an Artificial Intelligence (AI) model and an update model is provided; adopting a numerical model and an artificial intelligent model as data driving of a digital twin model to solve the problem of real-time mapping of a rotor test bed; the rotor test bed data is updated and corrected in the running process by updating the model and the real-time test data, so that the problem that errors of the real model and the digital twin model become larger gradually along with time is solved.
The invention adopts the following technical means:
a design method of a digital twin model test bed of an aero-engine rotor system comprises the following steps:
constructing a numerical model, calculating rotor dynamics characteristics and acquiring rotor dynamics data;
constructing an artificial intelligent model, inputting the rotor dynamics data acquired by the numerical model into the artificial intelligent model, and carrying out training prediction on the artificial intelligent model;
and constructing an updating model, and updating and correcting the data of the rotor test bed in the running process through the updating model and the real-time test data.
Further, the numerical model models the rotating shaft by using a Timoshenko beam unit, the disc is cylindrical into a centralized mass unit, the rotor system totally comprises 26 Timoshenko beam units and 4 disc units, and the gyro effect caused by rotation is considered when the rotor system rotates, so that the kinetic equation of the rotor system is as follows:
wherein M, G, C, K, Q, u represent rotor mass matrix, gyroscopic matrix, damping matrix, stiffness matrix, force and displacement values, respectively; therefore, the displacement value, the velocity value and the acceleration value of each point in the rotor system can be determined, and meanwhile, the critical rotation speed becomes an important parameter of dynamic characteristics, and can be obtained from the characteristic problems:
[K-λ 2 (M-jωG)]φ＝0
wherein lambda is the natural frequency corresponding to the critical rotation speed of the rotor system, phi is the vibration mode;
since unbalance occurs during operation, additional centrifugal force is generated:
F＝meω 2
wherein F represents centrifugal force, m represents centrifugal mass, e represents eccentric distance, and ω represents rotational angular velocity; thus, the kinetic equation for a rotor system under unbalanced conditions is as follows:
further, the artificial intelligence model predicts the dynamic characteristics of the rotor system in real time by adopting a Gaussian process regression model.
Further, the general model of the gaussian process regression model for the regression problem is expressed as:
wherein the relation between x and y in the regression model is represented by an arbitrarily hypothesized function f (x), y= [ y ] 1 ,y 2 ,···,y n ] T Is a proper amount of n x 1-dimensional observation polluted by noise, epsilon is an observation noise vector which is mutually independent and obeys Gaussian distribution,
is the variance of noise, I n Is a unit array; x= [ x ] i,1 ,···,x i,d ] T (i＝1,2,···,n)，x∈R d Is an n x 1-dimensional random variable that obeys a gaussian distribution.
Further, the gaussian process regression model can accurately describe the function f (x) through learning of the observed data, and is uniquely determined by the mean function m (x) and the covariance function k (x, x), so the gaussian process regression model is further defined as:
f(x)GP(m(x),k(x,x))
wherein,,
further, the function f (x) is composed of a multidimensional gaussian distribution, and according to the property of the multidimensional gaussian distribution, the prior distribution of the observed value y is obtained by a general model definition formula of the gaussian process regression model and a further definition formula of the gaussian process regression model:
the average value is subtracted during data preprocessing to ensure that m (x) =0, and the observed value y and the output sample y are further obtained by the property of Gaussian distribution * Joint a priori distribution of predictors:
where k (x, x) is the covariance matrix of the output samples x and is a symmetric positive definite matrix of n×n, each element k (x i ,x j ) Represents x i And x j Is a correlation of (2); k (x, x) * )＝k(x * ,x) T Is the input sample x and the input value x to be predicted * An n x 1 covariance matrix therebetween; k (x) * ,x * ) For the input value x to be predicted * The variance of itself;
observed dataset d= { (x) consisting of x and y i ,y i ) I=1, 2, the number of the two groups, D is referred to as a training sample set or a learning sample set, under the obtained training set D condition, the posterior distribution of y is:
p(y * |D,x * )N(m(y * ),k(y * ,y * ))
wherein y is * The mean and variance of (c) are respectively:
wherein m (y) is the value x to be predicted * Corresponding output value y of (2) * Is the average value of (2); k (y) * ,y * ) Is the post of the output predicted valueThe variance can be used to measure the uncertainty of the predicted result.
Further, for the rotor dynamics data obtained by the numerical model calculation, m gaussian process regression models need to be established to predict the dynamics performance of the structure.
Further, the update model corrects the model parameter theta in real time according to real-time observation data k ＝(α k ,β k ) The updating model adopts Bayesian learning to merge prior information and likelihood information to realize reasoning of posterior information, and according to the Bayesian theorem, posterior distribution of model parameters can be expressed as:
wherein p (θ) k ) Representing prior distribution of k time step model parameters, which can be approximated by posterior distribution of k-1 time steps; l (y) k |θ k ) Representing likelihood probability, using gaussian likelihood:
wherein,,
a posterior evaluation value at time k-1; v is the uncertainty of the measurement system; f is a state equation, the expression of which is: />
Further, the design method of the digital twin model test bed of the aeroengine rotor system further comprises the step of constructing a 3D design module for obtaining topological structure of the rotor test bed equipment assembly and geometric description information of parts.
Further, the design method of the digital twin model test bed of the aeroengine rotor system further comprises the steps of constructing a virtual system module, and testing and evaluating specific characteristics of a product or service process in the virtual system based on the acquired topological structure of the rotor test bed equipment assembly and the geometric description information of the parts.
Compared with the prior art, the invention has the following advantages:
1. according to the design method of the digital twin model test bed of the aero-engine rotor system, a digital twin model modeling mode based on the combination of a numerical model, an Artificial Intelligence (AI) model and an update model is provided for the physical structure of the rotor test bed; the whole process of the real-time mapping flow of the digital twin model and the physical entity can be realized, the real-time mapping of the rotor test bed entity and the digital twin model is realized, the vibration characteristic of the rotor system is truly reflected, the test risk is reduced, and the influence mechanism is revealed;
2. according to the design method of the digital twin model test bed of the aero-engine rotor system, which is provided by the invention, a numerical model and an artificial intelligent model are adopted as data driving of the digital twin model, so that the real-time mapping problem of the rotor test bed is solved;
3. according to the design method of the digital twin model test bed of the aeroengine rotor system, provided by the invention, the data of the rotor test bed is updated and corrected in the running process by updating the model and the real-time test data, so that the problem that errors of the real model and the digital twin model become larger gradually along with time is solved.
Based on the reasons, the invention can be widely popularized in the fields of digital twinning and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a block diagram of a digital twin model test stand design process for an aircraft engine rotor system according to the present invention.
Fig. 2 is a node model of a rotor system according to an embodiment of the present invention.
FIG. 3 is a dynamic update model of rotor performance provided by an embodiment of the present invention.
Fig. 4 is a diagram of updating model data correction provided in an embodiment of the present invention.
Fig. 5 is a state monitoring diagram of a digital twin model according to an embodiment of the present invention.
Detailed Description
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The invention will be described in detail below with reference to the drawings in connection with embodiments.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The relative arrangement of the components and steps, numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise. Meanwhile, it should be clear that the dimensions of the respective parts shown in the drawings are not drawn in actual scale for convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail, but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any specific values should be construed as merely illustrative, and not a limitation. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further discussion thereof is necessary in subsequent figures.
In the description of the present invention, it should be understood that the azimuth or positional relationships indicated by the azimuth terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal", and "top, bottom", etc., are generally based on the azimuth or positional relationships shown in the drawings, merely to facilitate description of the present invention and simplify the description, and these azimuth terms do not indicate and imply that the apparatus or elements referred to must have a specific azimuth or be constructed and operated in a specific azimuth, and thus should not be construed as limiting the scope of protection of the present invention: the orientation word "inner and outer" refers to inner and outer relative to the contour of the respective component itself.
Spatially relative terms, such as "above … …," "above … …," "upper surface at … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations of "above … …" and "below … …". The device may also be positioned in other different ways (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In addition, the terms "first", "second", etc. are used to define the components, and are only for convenience of distinguishing the corresponding components, and the terms have no special meaning unless otherwise stated, and therefore should not be construed as limiting the scope of the present invention.
The invention provides a design method of a digital twin model test bed of an aero-engine rotor system, which comprises the following steps:
constructing a numerical model, calculating rotor dynamics characteristics and acquiring rotor dynamics data;
constructing an artificial intelligent model, inputting the rotor dynamics data acquired by the numerical model into the artificial intelligent model, and carrying out training prediction on the artificial intelligent model;
and constructing an updating model, and updating and correcting the data of the rotor test bed in the running process through the updating model and the real-time test data.
Based on the design method of the digital twin model test bed of the aero-engine rotor system, the embodiment of the invention also provides the digital twin model test bed of the aero-engine rotor system, which is shown in fig. 1 and comprises a 3D design module, a virtual system module and a data processing module, wherein:
and the 3D design module is used for acquiring topological structure and part geometric description information of the rotor test bed equipment assembly.
And the virtual system module is used for showing dynamic characteristics based on the acquired topological structure of the rotor test bed equipment assembly and the geometric description information of the parts, and testing and evaluating specific characteristics of a product or service process in the virtual system.
The data processing module is used as a data driving core module of the digital twin model and consists of a numerical model, an artificial intelligent model and an updating model. The numerical model is used for calculating the dynamic characteristics of the rotor test bed, the artificial intelligent model is used for simulating the training prediction of the calculation data, and the update model is used for correcting the predicted data of the artificial intelligent model.
In specific implementation, as a preferred embodiment of the present invention, the numerical model models the rotating shaft by using Timoshenko beam units, and the disc is cylindrical into a centralized mass unit, and the rotor system includes 26 Timoshenko beam units and 4 disc units, as shown in fig. 2, when the rotor system rotates, gyroscopic effects caused by rotation are considered, so the kinetic equation of the rotor system is as follows:
wherein M, G, C, K, Q, u represent rotor mass matrix, gyroscopic matrix, damping matrix, stiffness matrix, force and displacement values, respectively; therefore, the displacement value, the velocity value and the acceleration value of each point in the rotor system can be determined, and meanwhile, the critical rotation speed becomes an important parameter of dynamic characteristics, and can be obtained from the characteristic problems:
[K-λ 2 (M-jωG)]φ＝0
wherein lambda is the natural frequency corresponding to the critical rotation speed of the rotor system, phi is the vibration mode;
since unbalance occurs during operation, additional centrifugal force is generated:
F＝meω 2
wherein F represents centrifugal force, m represents centrifugal mass, e represents eccentric distance, and ω represents rotational angular velocity; thus, the kinetic equation for a rotor system under unbalanced conditions is as follows:
in particular, as a preferred embodiment of the present invention, the artificial intelligence model uses a gaussian process regression model (Gaussian processes regression, GPR) to predict the dynamic characteristics of the rotor system in real time. Gaussian process regression is a regression algorithm with high and non-linear problems for the input. The regression analysis method is a statistical analysis method for determining the quantitative relationship of the interdependence between two or more variables, namely the dependent variable y and the independent variable x, and the general model of the Gaussian process regression model aiming at the regression problem is expressed as follows:
wherein the relation between x and y in the regression model is represented by an arbitrarily hypothesized function f (x), y= [ y ] 1 ,y 2 ,···,y n ] T Is a proper amount of n x 1-dimensional observation polluted by noise, epsilon is an observation noise vector which is mutually independent and obeys Gaussian distribution,
is the variance of noise, I n Is a unit array; x= [ x ] i,1 ,···,x i,d ] T (i＝1,2,···,n)，x∈R d Is an n x 1-dimensional random variable that obeys a gaussian distribution.
The gaussian process regression model, which is uniquely determined by the mean function m (x) and the covariance function k (x, x), can accurately describe the function f (x) through learning of the observed data, and is therefore further defined as:
f(x)GP(m(x),k(x,x))
wherein,,
the function f (x) is composed of a multidimensional Gaussian distribution, and according to the property of the multidimensional Gaussian distribution, the prior distribution of the observed value y is obtained by a general model definition formula of the Gaussian process regression model and a further definition formula of the Gaussian process regression model, wherein the prior distribution is as follows:
the mean value is subtracted during data preprocessing, so that m (x) =0, and the combined prior distribution of the observed value y and the predicted value of the output sample y is further obtained by the property of Gaussian distribution:
where k (x, x) is the covariance matrix of the output samples x and is a symmetric positive definite matrix of n×n, each element k (x i ,x j ) Represents x i And x j Is a correlation of (2); k (x, x) * )＝k(x * ,x) T Is the input sample x and the input value x to be predicted * An n x 1 covariance matrix therebetween; k (x) * ,x * ) For the input value x to be predicted * The variance of itself;
observed dataset d= { (x) consisting of x and y i ,y i ) I=1, 2, the number of the two groups, D is referred to as a training sample set or a learning sample set, under the obtained training set D condition, the posterior distribution of y is:
p(y * |D,x * )N(m(y * ),k(y * ,y * ))
wherein y is * The mean and variance of (c) are respectively:
wherein m (y * ) For the value x to be predicted * Corresponding output value y of (2) * Is the average value of (2); k (y) * ,y * ) The post-test variance of the output predicted value can be used to measure the uncertainty, also referred to as the confidence level, of the predicted result. This is also an advantage of GPR over neural network (BP) and Support Vector Machine (SVM) methods.
In specific implementation, as a preferred embodiment of the present invention, for the rotor dynamics data obtained by calculation of the numerical model, m gaussian process regression models need to be built to predict the dynamics performance of the structure.
Concrete embodimentsIn implementation, as a preferred embodiment of the invention, real-time mapping is realized between the twin model and the physical object through data communication in the digital twin, and the digital twin model is not static description of the physical object at a certain moment, but is driven by data to enable the twin model to follow the change of the physical entity along with time, so that the physical object at any time section is dynamically described. The trained prediction model is used for real-time mapping, and accuracy in the running process is guaranteed by matching with the updated model. For the established digital twin model, the purpose of model update is to correct model parameters theta in real time according to real-time observation data k ＝(α k ,β k ) Is a probability distribution of (c). Bayesian learning is a machine learning method based on probability statistics, and is widely applied to the problem of uncertainty reasoning due to the structural specificity of the machine learning method. The Bayesian learning fuses the prior information and the likelihood information to realize the reasoning of the posterior information as shown in figure 3. In this embodiment, the update model adopts bayesian learning to fuse prior information and likelihood information to implement reasoning on posterior information, and according to bayesian theorem, posterior distribution of model parameters can be expressed as:
wherein p (θ) k ) Representing prior distribution of k time step model parameters, which can be approximated by posterior distribution of k-1 time steps; l (y) k |θ k ) Representing likelihood probability, using gaussian likelihood:
wherein,,
a posterior evaluation value at time k-1; v is the uncertainty of the measurement system; f is a state equation, the expression of which is: />
In summary, compared with the existing digital twin modeling method, the method can realize the whole process of the real-time mapping flow of the digital twin model and the physical entity, realize the real-time mapping of the rotor test bed entity and the digital twin model, truly reflect the vibration characteristics of the rotor system, and update the model and the real-time test data, so that the rotor test bed data is updated and corrected in the operation process, and as shown in fig. 4, the problem that errors of the real model and the digital twin model become larger gradually along with time is solved. Meanwhile, high-precision real-time mapping of maximum vibration displacement of the rotor test bed at different rotating speeds can be realized, and the effect is shown in fig. 5.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (10)
1. The design method of the digital twin model test bed of the aero-engine rotor system is characterized by comprising the following steps of:
constructing a numerical model, calculating rotor dynamics characteristics and acquiring rotor dynamics data;
constructing an artificial intelligent model, inputting the rotor dynamics data acquired by the numerical model into the artificial intelligent model, and carrying out training prediction on the artificial intelligent model;
and constructing an updating model, and updating and correcting the data of the rotor test bed in the running process through the updating model and the real-time test data.
2. The method for designing a digital twin model test stand for an aircraft engine rotor system according to claim 1, wherein the numerical model models a rotating shaft by using Timoshenko beam units, and the rotating shaft is cylindrical into a centralized mass unit, the rotor system comprises 26 Timoshenko beam units and 4 disk units in total, and the gyro effect caused by rotation is considered when the rotor system rotates, so that a kinetic equation of the rotor system is:
wherein M, G, C, K, Q, u represent rotor mass matrix, gyroscopic matrix, damping matrix, stiffness matrix, force and displacement values, respectively; therefore, the displacement value, the velocity value and the acceleration value of each point in the rotor system can be determined, and meanwhile, the critical rotation speed becomes an important parameter of dynamic characteristics, and can be obtained from the characteristic problems:
[K-λ 2 (M-jωG)]φ＝0
wherein lambda is the natural frequency corresponding to the critical rotation speed of the rotor system, phi is the vibration mode;
since unbalance occurs during operation, additional centrifugal force is generated:
F＝meω 2
wherein F represents centrifugal force, m represents centrifugal mass, e represents eccentric distance, and ω represents rotational angular velocity; thus, the kinetic equation for a rotor system under unbalanced conditions is as follows:
3. the method for designing a digital twin model test stand for an aircraft engine rotor system according to claim 1, wherein the artificial intelligence model predicts the dynamic characteristics of the rotor system in real time by using a gaussian process regression model.
4. The method for designing a digital twin model test stand for an aircraft engine rotor system according to claim 3, wherein the general model of the gaussian process regression model for the regression problem is expressed as:
wherein the relation between x and y in the regression model is represented by an arbitrarily hypothesized function f (x), y= [ y ] 1 ,y 2 ,···,y n ] T Is a proper amount of n x 1-dimensional observation polluted by noise, epsilon is an observation noise vector which is mutually independent and obeys Gaussian distribution,
is the variance of noise, I n Is a unit array; x= [ x ] i,1 ,···,x i,d ] T (i＝1,2,···,n)，x∈R d Is an n x 1-dimensional random variable that obeys a gaussian distribution.
5. The aircraft engine rotor system digital twin model bench design method according to claim 4, wherein the gaussian process regression model accurately depicts the function f (x) through the learning of the observed data, and the gaussian process regression model is uniquely determined by the mean function m (x) and the covariance function k (x, x), and therefore, the gaussian process regression model is further defined as:
f(x)GP(m(x),k(x,x))
wherein,,
6. the method for designing a digital twin model test stand for an aircraft engine rotor system according to claim 5, wherein the function f (x) is composed of a multidimensional gaussian distribution, and the prior distribution of the observed value y is obtained by a general model definition formula of the gaussian process regression model and a further definition formula of the gaussian process regression model according to the properties of the multidimensional gaussian distribution, wherein the prior distribution is:
the average value is subtracted during data preprocessing to ensure that m (x) =0, and the observed value y and the output sample y are further obtained by the property of Gaussian distribution * Joint a priori distribution of predictors:
where k (x, x) is the covariance matrix of the output samples x and is a symmetric positive definite matrix of n×n, each element k (x i ,x j ) Represents x i And x j Is a correlation of (2); k (x, x) * )＝k(x * ,x) T Is the input sample x and the input value x to be predicted * An n x 1 covariance matrix therebetween; k (x) * ,x * ) For the input value x to be predicted * The variance of itself;
observed dataset d= { (x) consisting of x and y i ,y i ) I=1, 2, the number of the two groups, D is referred to as a training sample set or a learning sample set, under the condition of the obtained training set D, y * The posterior distribution of (2) is:
p(y * |D,x * )N(m(y * ),k(y * ,y * ))
wherein y is * The mean and variance of (c) are respectively:
wherein m (y * ) For the value x to be predicted * Corresponding output value y of (2) * Is the average value of (2); k (y) * ,y * ) Is the post-test variance of the output predicted value and can be used to measure the uncertainty of the predicted result.
7. The method for designing a digital twin model test stand for an aircraft engine rotor system according to claim 5, wherein for the rotor dynamics data obtained by the numerical model calculation, m gaussian process regression models are required to be established to predict the dynamics of the structure.
8. The method for designing a digital twin model test stand for an aircraft engine rotor system according to claim 1, wherein the update model corrects model parameters θ in real time based on real-time observation data k ＝(α k ,β k ) The updating model adopts Bayesian learning to merge prior information and likelihood information to realize reasoning of posterior information, and according to the Bayesian theorem, posterior distribution of model parameters can be expressed as:
wherein p (θ) k ) Representing prior distribution of k time step model parameters, which can be approximated by posterior distribution of k-1 time steps; l (y) k |θ k ) Representing likelihood probability, using gaussian likelihood:
wherein,,
a posterior evaluation value at time k-1; v is the uncertainty of the measurement system; f is a state equation, the expression of which is: />
9. The aircraft engine rotor system digital twin model test stand design method of claim 1, further comprising constructing a 3D design module for obtaining rotor test stand rig assembly topology and part geometry description information.
10. The aircraft engine rotor system digital twin model test stand design method of claim 1, further comprising constructing a virtual system module for testing and evaluating specific features of a product or service process in a virtual system based on acquired rotor test stand equipment assembly topology and part geometry descriptive information, exhibiting dynamics.
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