Model correction method and related equipment

Abstract

The invention provides a model correction method and related equipment, and the method comprises the steps: solving a finite element model of an aircraft, obtaining a full-degree-of-freedom finite element vibration mode, carrying out the extension of a test vibration mode of the aircraft according to the finite element vibration mode, obtaining a full-degree-of-freedom extension vibration mode, and carrying out the calculation of the full-degree-of-freedom extension vibration mode. Therefore, comprehensive aircraft vibration mode data with relatively high accuracy can be obtained; and then the aircraft finite element model is corrected through the extended vibration mode to obtain the aircraft finite element model conforming to the experimental data, so that more accurate mechanical simulation can be performed on the aircraft, and the reliability of a simulation result is improved.

Description

Technical Field

[0001] The present application relates to the technical field of finite element simulation, and in particular to a model correction method and related equipment. Background Art

[0002] The finite element method has been widely used in engineering fields such as aerospace. Establishing a reasonable and accurate structural finite element model plays a vital role in structural dynamics analysis and design. However, there will inevitably be deviations between the finite element model and the engineering structure. These differences may come from the deviation of the actual structure from the original design during manufacturing, processing, assembly and connection, and unreasonable approximation or equivalence of the structure during the modeling process. Therefore, it is imperative to develop an effective model correction method, that is, to improve the accuracy of the finite element model by obtaining modal data through experiments.

[0003] Model correction methods are generally divided into direct methods and iterative methods. Iterative correction methods usually choose to correct the target structural parameters to improve the correlation between the test measurement data and the analysis model. The direct correction method generally directly corrects the stiffness matrix and mass matrix of the structure, which can avoid iterative calculation and subjective correction parameter selection, and eliminate the possibility of calculation divergence and large amount of calculation. However, there are still two problems in the current research: 1) Under the current level of testing technology, it is generally believed that the natural frequency measurement of the structure is accurate, and the measured vibration mode of the structure is considered to be incomplete and erroneous. In the correction process, the measured vibration mode needs to be expanded and matched with the degrees of freedom of the finite element model. The measurement error will be further amplified in the vibration mode expansion, reducing the accuracy of model correction; 2) Since the measured modal data is generally incomplete, under the premise of ensuring the reproduction of low-level test modal data, it is necessary to ensure that the high-order modes of the structure and the symmetric positive definite properties of the corrected stiffness matrix and mass matrix do not change. Therefore, in view of the above problems, it is of great theoretical and practical significance to develop modal expansion technology that considers the influence of measurement noise and direct model correction methods without overflow. Summary of the invention

[0004] In view of this, the purpose of this application is to propose a model correction method and related equipment.

[0005] Based on the above purpose, the present application provides a model correction method, wherein the model is an aircraft finite element model. The method comprises: solving the vibration mode of the aircraft finite element model to obtain the full-degree-of-freedom finite element vibration mode. Obtaining the test vibration mode, expanding the test vibration mode according to the finite element method to obtain the extended vibration mode. Correcting the aircraft finite element model according to the extended vibration mode to obtain a corrected model, wherein the corrected model is used to perform finite element simulation of the aircraft.

[0006] In some embodiments, the test vibration mode is expanded according to the finite element method to obtain the expanded vibration mode, which specifically includes: solving the partial transformation matrix of the corresponding degree of freedom according to the finite element vibration mode of the degree of freedom corresponding to the test vibration mode. The partial transformation matrix is ​​solved by the following formula: in, represents the pseudo-inverse of the finite element vibration mode of the aircraft, ψ mj Represents the test vibration shape. Fit the partial transformation matrix to obtain the fitting transformation matrix. Expand the test vibration shape according to the fitting transformation matrix.

[0007] In some embodiments, fitting a portion of the conversion matrix to obtain a fitting conversion matrix specifically includes: constructing a noise vector, constructing a fitting extended vibration shape according to the noise vector, solving the fitting conversion matrix according to the Bayesian theorem, and the extended vibration shape is represented by the following formula: j=1,2,…r. Among them, Represents the extended vibration mode after expansion by the fitted transformation matrix. Represents the finite element mode shapes of the vehicle including the fitted degrees of freedom. Represents the fitted transformation matrix. ∈ j represents the noise vector, subject to

[0008] In some embodiments, solving the fitting transformation matrix according to the Bayesian theorem specifically includes: constructing a Gaussian approximation function of the extended vibration shape according to the noise vector and the extended vibration shape. Solving the prior and the posterior of the fitted extended vibration shape according to the Bayesian theorem. Solving the extended vibration shape according to the prior and the posterior. The Gaussian approximation function is represented by the following formula: The prior is expressed by the following formula: in, The posterior is expressed by the following formula:

[0009] In some embodiments, after solving the fitting conversion matrix according to the Bayesian theorem, the method further includes: calculating a MAC value according to the extended vibration shape and the test vibration shape. Verifying the fitting of the extended vibration shape according to the MAC value. The MAC value is calculated by the following formula: Among them, ψ mj,fit represents the extended vibration mode. mj，obs Represents the test vibration mode.

[0010] In some embodiments, the aircraft finite element model is modified according to the extended vibration mode, specifically including: constructing the generalized eigenvalue equation of the mass matrix and the stiffness matrix according to the aircraft finite element vibration mode. The generalized eigenvalue equation is modified according to the extended vibration mode. The generalized eigenvalue equation of the mass matrix and the stiffness matrix is ​​expressed by the following formula: in, represents the stiffness matrix. Represents the eigenvalues ​​of the first r orders of any N×N matrix A. Represents the Nrth-order eigenvalue of any N×N matrix A. Φ a Represents the first r-order finite element vibration mode of the aircraft. Φ b represents the finite element vibration mode of the Nrth-order aircraft. M represents the mass matrix.

[0011] In some embodiments, the aircraft finite element model is modified according to the extended vibration mode, specifically including: constructing a first matrix according to the extended vibration mode, solving the first matrix according to the aircraft finite element vibration mode. Modifying the mass matrix and the stiffness matrix according to the first matrix. The first matrix is ​​represented by the following formula: in, represents the inverse of the first matrix. Φ FE Represents the finite element vibration mode of the N-th order aircraft.

[0012] The present application also provides a model correction device, wherein the model is a finite element model of an aircraft. The device includes: a model solving module, which is used to solve the vibration mode of the aircraft finite element model to obtain the full-degree-of-freedom finite element vibration mode. A vibration mode expansion module, which is used to obtain the test vibration mode, expand the test vibration mode according to the finite element method, and obtain the extended vibration mode. A model correction module, which is used to correct the aircraft finite element model according to the extended vibration mode to obtain a corrected model, wherein the corrected model is used to perform finite element simulation of the aircraft.

[0013] The present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements any one of the above methods when executing the program.

[0014] The present application also provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable a computer to execute any of the above methods.

[0015] From the above, it can be seen that the model correction method provided in the present application solves the finite element model of the aircraft to obtain the finite element vibration mode with full degrees of freedom, and then expands the experimental vibration mode of the aircraft according to the finite element vibration mode to obtain the extended vibration mode with full degrees of freedom, thereby obtaining aircraft vibration mode data with high accuracy and comprehensiveness; the finite element model of the aircraft is then corrected by the extended vibration mode to obtain the finite element model of the aircraft that is consistent with the experimental data, so that more accurate mechanical simulation of the aircraft can be performed, thereby improving the reliability of the simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present application or related technologies, the drawings required for use in the embodiments or related technical descriptions are briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 A schematic diagram of a flow chart of a model correction method provided in an embodiment of the present application;

[0018] Figure 2 A schematic diagram of a flow chart of a vibration mode expansion method provided in an embodiment of the present application;

[0019] Figure 3 A schematic diagram of a flow chart of a method for solving a transformation matrix provided in an embodiment of the present application;

[0020] Figure 4 A schematic diagram of a flow chart of an extended vibration mode solving method provided in an embodiment of the present application;

[0021] Figure 5 A schematic diagram of a flow chart of a vibration mode fitting verification method provided in an embodiment of the present application;

[0022] Figure 6 A schematic flow chart of a generalized characteristic equation correction method provided in an embodiment of the present application;

[0023] Figure 7 A flow chart of a method for correcting a mass matrix and a stiffness matrix provided in an embodiment of the present application;

[0024] Figure 8 A schematic diagram of a simplified launch vehicle model solved according to the method of the present application;

[0025] Fig. 9 A schematic diagram of the first six vibration modes of a simplified launch vehicle test model solved according to the method of this application;

[0026] Fig.10 A schematic diagram of the structure of a model correction device provided in an embodiment of the present application;

[0027] Fig.11 A more specific schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0028] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0029] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should be the usual meanings understood by people with ordinary skills in the field to which the present application belongs. The "first", "second" and similar words used in the embodiments of the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing in front of the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0030] The present application provides a model correction method, wherein the model is an aircraft finite element model.

[0031] like Figure 1 As shown, the method includes:

[0032] Step S1, solving the vibration mode of the aircraft finite element model to obtain the full-degree-of-freedom finite element vibration mode.

[0033] Step S2, obtaining a test vibration shape, and expanding the test vibration shape according to the finite element method to obtain an expanded vibration shape.

[0034] Step S3, modifying the aircraft finite element model according to the extended vibration mode to obtain a modified model, wherein the modified model is used to perform finite element simulation on the aircraft.

[0035] In this embodiment, in the manufacturing process, due to the influence of raw materials and production processes, there are differences between the actual vibration parameters of the aircraft and the idealized model calculated in the finite element model. In order to improve the accuracy of the finite element simulation, it is necessary to make appropriate adjustments to the aircraft finite element model in combination with the actual vibration test parameters so that the simulation results of the aircraft finite element model are closer to the actual model.

[0036] Among them, by solving the vibration mode of the aircraft finite element model, the vibration mode data of the aircraft corresponding to the ideal state is obtained. At this time, it is assumed that the finite element vibration mode has N degrees of freedom and the natural frequency is ω i , i = 1, 2, ... N, then the full degree of freedom finite element vibration mode is expressed as The vibration mode corresponding to the measured degree of freedom is

[0037] Since the vibration test of the aircraft cannot fully test the vibration modes of all degrees of freedom of the aircraft, it is necessary to expand the incomplete test vibration mode according to the finite element vibration mode to obtain the extended vibration mode. The incomplete test vibration mode is expressed as The corresponding relationship between the finite element vibration mode and the experimental vibration mode completed by the test can be solved, and the transformation matrix can be defined according to the corresponding relationship, and the experimental vibration mode can be expanded through the transformation matrix.

[0038] The finite element model can be further modified according to the expanded test vibration mode, so that the force conditions of the aircraft in the actual application scenario can be accurately simulated through the modified finite element model.

[0039] In some embodiments, Figure 2 As shown, step S2 specifically includes:

[0040] Step S21, solving a partial transformation matrix corresponding to the degree of freedom according to the finite element vibration mode of the test vibration mode corresponding to the degree of freedom.

[0041] The partial transformation matrix is ​​solved by the following formula:

[0042]

[0043] in, represents the pseudo-inverse of the finite element vibration mode of the aircraft, ψm j Represents the test vibration mode.

[0044] Step S22, fitting a part of the transformation matrix to obtain a fitting transformation matrix.

[0045] Step S23, expanding the test vibration mode according to the fitting transformation matrix.

[0046] In this embodiment, it can be seen from the system equivalent condensation and expansion processing method that the first r-order experimental vibration mode ψ mj , j = 1, 2, ... r can be obtained by the vibration mode Φ of the finite element model m The linear combination is expressed as follows: the transformation matrix P j Defined as

[0047] ψ mj =Φ m P j , j = 1, 2, ... r

[0048] The overall finite element vibration mode Φ can be used FE To expand the test vibration mode, the expanded vibration mode formula is expressed as:

[0049] ψ j =Φ FE P j , j = 1, 2, ... r

[0050] By transforming the matrix P j Solve to obtain the corresponding extended vibration mode.

[0051] In some embodiments, Figure 3 As shown, step S22 specifically includes:

[0052] Step S201, constructing a noise vector, and constructing a fitting extended vibration shape according to the noise vector.

[0053] Step S202, solving the fitting transformation matrix according to Bayesian theorem.

[0054] The extended mode shape is expressed by the following formula:

[0055]

[0056] in, Represents the extended vibration mode after expansion by the fitted transformation matrix. Represents the finite element mode shapes of the vehicle including the fitted degrees of freedom. Represents the fitted transformation matrix. ∈ j represents the noise vector, subject to

[0057] In this embodiment, in the process of obtaining the test vibration mode, since the test vibration mode will be affected by noise to a certain extent, the conversion matrix obtained by directly solving the correspondence between the test vibration mode and the finite element vibration mode will produce a certain degree of numerical error. Therefore, it is necessary to compensate for the solution of the conversion matrix by the local correspondence method, and re-express the extended vibration mode as follows:

[0058]

[0059] in, From the finite element vibration mode Φ m Selected from j To avoid overfitting, the test vibration shape ψ mj Divided into fitting groups ψ mj,fit and the observation group ψ mj,obs , fitting group ψ mj,fit Used to solve the fitting transformation matrix It is expressed as:

[0060]

[0061] in, Φ fit represents the finite element mode shape including the fitted degrees of freedom, from which the extended mode shape is calculated:

[0062]

[0063] By introducing a noise-related vector ∈ j , and finally the extended vibration shape is expressed as The calculation results in a more accurate extended vibration mode.

[0064] Among them, ∈ j is modeled probabilistically as zero mean with unknown variance σ 2 Gaussian distribution, that is, ∈ j obey I represents the identity matrix.

[0065] In some embodiments, Figure 4 As shown, step S202 specifically includes:

[0066] Step S211: constructing a Gaussian approximation function of the extended vibration shape according to the noise vector and the extended vibration shape.

[0067] Step S212, solving the priori and the posterior of the fitted extended vibration mode according to the Bayesian theorem.

[0068] Step S213, solving the extended vibration mode according to the priori and the a posteriori.

[0069] Among them, the Gaussian approximation function is expressed by the following formula:

[0070]

[0071] The prior is expressed by the following formula:

[0072]

[0073] in,

[0074] The posterior is expressed by the following formula:

[0075]

[0076] In this embodiment, the prior marginal likelihood Can be The Gaussian likelihood function and P j，s The a priori integral is obtained, and the calculation according to the a priori formula can be obtained:

[0077]

[0078] According to the Bayesian formula, we can calculate the posterior:

[0079]

[0080] in,

[0081] in, and Respectively The covariance and mean of . The mean This is the required transformation matrix.

[0082] In some embodiments, Figure 5 As shown, after step S202, the method further includes:

[0083] Step S203, calculating the MAC value according to the extended vibration mode and the test vibration mode.

[0084] Step S204: verify the fitting of the extended vibration mode according to the MAC value.

[0085] The MAC value is calculated by the following formula:

[0086]

[0087] Among them, ψ mj,fit represents the extended vibration mode. mj,obs Represents the test vibration mode.

[0088] In this embodiment, by calculating ψ mj,obs With extended modal The vector containing the degrees of freedom for the experiment The MAC value was used to check the quality of the fit.

[0089] Among them, through inspection The value can be used to determine the matching degree between the observation group and the extended vibration mode. The closer the value is to 1, the better the match between the observed group and the extended vibration mode, that is, the higher the fitting quality. First, the vibration mode Φ fit Sort by the frequency range between the mode and the corresponding test mode. fit,1 ,Φ fit,2 ,…(where Φ fit,1 Contains the sorted first-order vibration mode, Φ fit,2 Contains the first two order vibration modes after sorting, ...), repeats the expansion and MAC value verification operations, according to value, to obtain the optimal So as to obtain the optimal extended test mode

[0090] In some embodiments, Figure 6 As shown, step S3 specifically includes:

[0091] Step S31, constructing the generalized eigenvalue equations of the mass matrix and the stiffness matrix according to the finite element vibration mode of the aircraft.

[0092] Step S32, correcting the generalized eigenvalue equation according to the extended vibration mode.

[0093] The generalized eigenvalue equations of the mass matrix and the stiffness matrix are expressed by the following formula:

[0094]

[0095] in, represents the stiffness matrix. Represents the eigenvalues ​​of the first r orders of any N×N matrix A. Represents the Nrth-order eigenvalue of any N×N matrix A. Φ a Represents the first r-order finite element vibration mode of the aircraft. Φ b represents the finite element vibration mode of the Nrth-order aircraft. M represents the mass matrix.

[0096] In this embodiment, according to Brauer's theorem (Brauer-Suzuki theorem) and its generalization, the relationship between the eigenvalues ​​of a given square matrix A and its update matrix is ​​proved. For any N×N matrix A, and Φ FE =[φ1,φ2,…,φ N ] are its eigenvalue and right eigenvector respectively. Take the first r groups of eigenpairs to form the matrix and Φ a =[φ1,φ2,…,φ r ], and then Nr groups of feature pairs form the matrix and Φ b =[φ r+1 ,φ r+2 ,…,φ N ], B is an arbitrary r×N matrix. Then the matrix The characteristic value of in is the matrix Λ a +BΦ a The eigenvalues ​​of and define

[0097] Let A = M -1 K, but

[0098] in and Φ b =[Φ r+1 ,φ r+2 ,…,Φ N ] are the characteristic pair matrices of the Nr groups respectively. Substitution In the equation, we can get the increment ΔK of the stiffness matrix as

[0099]

[0100] According to the above formula, the modified stiffness matrix is ​​obtained and the generalized eigenvalue equation of the mass matrix M.

[0101] In some embodiments, Figure 7 As shown, step S32 specifically includes:

[0102] Step S301, constructing a first matrix according to the extended vibration mode, and solving the first matrix according to the aircraft finite element vibration mode.

[0103] Step S302: correcting the mass matrix and the stiffness matrix according to the first matrix.

[0104] The first matrix is ​​represented by the following formula:

[0105]

[0106] in, represents the inverse of the first matrix. Φ FE Represents the finite element vibration mode of the N-th order aircraft.

[0107] In this embodiment, due to the vibration mode Φ FE The mass matrix M is orthogonal. In order to modify the vibration mode Φ of the finite element model a , introduce the first matrix

[0108] in, is any reversible matrix satisfying Then the final updated stiffness matrix and mass matrix can be written as:

[0109]

[0110] By solving the first matrix The updated stiffness matrix and quality matrix The generalized eigenvalue equation of can be approximately expressed as

[0111]

[0112] Thus, the stiffness matrix of the finite element model is completed by setting the natural frequency and vibration mode separately. and quality matrix Direct correction can avoid optimization iteration and subjective correction parameter selection while maintaining high correction accuracy and efficiency, and effectively reduce the modeling error of actual engineering structures.

[0113] It can be seen from the above embodiments of the present application that the present application obtains the finite element vibration mode with full degrees of freedom by solving the finite element model of the aircraft, and then expands the experimental vibration mode of the aircraft according to the finite element vibration mode to obtain the expanded vibration mode with full degrees of freedom, thereby obtaining aircraft vibration mode data with high accuracy and comprehensiveness; and then corrects the aircraft finite element model through the expanded vibration mode to obtain the aircraft finite element model that is consistent with the experimental data, thereby enabling more accurate mechanical simulation of the aircraft and improving the reliability of the simulation results.

[0114] This application also introduces noise data and solves the extended vibration mode through Bayesian theorem, which has high accuracy and noise resistance.

[0115] The present application also modifies the finite element model according to the extended vibration mode. The natural frequency of the modified model can be consistent with the test results, and even if there is the influence of measurement errors, the modified vibration mode can maintain a high degree of accuracy.

[0116] According to the model correction method provided in this application, a simplified launch vehicle (such as Figure 8 The model modification of the booster and the core stage is taken as an example to verify the method of this application. The equivalent beam model of each booster and the entire core stage consists of 10 BEAM188 units, 10 COMBIN14 units, 10 mass points and 11 nodes, and a fixed constraint is applied at the bottom. The damping ratio of the structure is 0.01. The connection between the booster and the core stage (as shown in Figure 8 The BEAM188 beam element is used for equivalent (shown by the red line in the middle). In the finite element model, the elastic modulus and density of these eight connections are 2×10 11 Pa and 7850kg / m 3 For the test model, the elastic modulus and density of the eight connections are 2.4×10 11 Pa and 7050kg / m 3 , and the rest of the structural parameters are the same as those of the finite element model. Fig. 9 The schematic diagram of the first 6 vibration modes of the simplified launch vehicle test model is shown. The first 16 natural frequencies under the test model and the corresponding measurement point locations (such as Figure 8 The vibration modes of the degrees of freedom in the x, y, and z directions (shown by the red and blue dots in the middle) are used as the modal test results, among which the degrees of freedom at the red measuring point are used as the fitting group ψ mj,fit , the blue point degrees of freedom are used as the observation group ψ mj,obs ,j=1,2,…,16.

[0117] The calculation steps include:

[0118] 1. First, the simplified launch vehicle model is analyzed by real eigenvalue using commercial software. The first 30 natural frequencies and all degrees of freedom vibration modes of the structural finite element model to be corrected are obtained; the first 16 natural frequencies and partial vibration modes of the degrees of freedom of the test model are obtained, and different levels of noise are added to simulate the real modal test results; the first 16 degrees of freedom vibration modes of the test model are obtained for comparison to verify the effectiveness of the proposed model correction method.

[0119] 2. Using the correlation vector regression algorithm, the transformation matrix corresponding to each order vibration mode is calculated under the Bayesian framework, and the optimal test vibration mode containing all degrees of freedom after expansion is obtained. Without considering the measurement noise, the MAC value between the expanded test vibration mode and the vibration mode of the real test model is compared, as shown in Table 1.

[0120] 3. Based on the natural frequency of the test model and the complete test vibration shape ψ obtained by the expansion of the correlation vector regression algorithm, the natural frequency and vibration shape of the finite element model are partially set to obtain the stiffness matrix and mass matrix of the modified structure. Through eigenvalue analysis, the natural frequency and vibration shape of the modified structure are calculated and compared with the natural frequency and vibration shape of the test model. The results are shown in Table 1. It can be found that after correction, the natural frequency of the structure can also be consistent with the test model; for MAC, the vibration shape ψ containing all degrees of freedom obtained after expansion and the vibration shape φ corresponding to the modified model up , which are consistent with the actual test structure vibration mode φ T Have a higher degree of matching.

[0121] Table 1 Comparison of structural natural frequency and MAC

[0122]

[0123] 4. According to steps 1-3, further exploration is conducted to give the comparison results of the proposed method and the LC method under the vibration mode of 5% noise level measurement. It can be found that the natural frequency of the corrected model is not affected by noise and is always consistent with the test model, as shown in Table 1. The comparison of MAC values ​​is given in Table 2, and it can be found that the modal expansion results and model correction results of the proposed method have higher accuracy and stronger noise resistance.

[0124] Table 2 Comparison of MAC between the method of the present invention and the LC method at 5% noise level

[0125]

[0126] It should be noted that the method of the embodiment of the present application can be performed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present application, and the multiple devices will interact with each other to complete the described method.

[0127] It should be noted that the above describes some embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0128] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a model correction device.

[0129] refer to Fig.10 , the model correction device comprises:

[0130] The model solving module 401 is used to solve the vibration mode of the aircraft finite element model to obtain the full-degree-of-freedom finite element vibration mode.

[0131] The vibration mode expansion module 402 is used to obtain the test vibration mode, expand the test vibration mode according to the finite element method, and obtain the expanded vibration mode.

[0132] The model correction module 403 is used to correct the aircraft finite element model according to the extended vibration mode to obtain a corrected model, wherein the corrected model is used to perform finite element simulation on the aircraft.

[0133] For the convenience of description, the above device is described in terms of functions divided into various modules. Of course, when implementing the present application, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0134] The device of the above embodiment is used to implement the corresponding model correction method in any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0135] Based on the same inventive concept, corresponding to any of the above-mentioned embodiments and methods, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the model correction method described in any of the above embodiments is implemented.

[0136] Fig.11 A more specific schematic diagram of the hardware structure of an electronic device provided in this embodiment is shown, and the device may include: a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040 are connected to each other through the bus 1050 in the device.

[0137] The processor 1010 can be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0138] The memory 1020 may be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 may store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program codes are stored in the memory 1020 and are called and executed by the processor 1010.

[0139] The input / output interface 1030 is used to connect the input / output module to realize information input and output. The input / output module can be configured in the device as a component (not shown in the figure), or it can be externally connected to the device to provide corresponding functions. The input device may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output device may include a display, a speaker, a vibrator, an indicator light, etc.

[0140] The communication interface 1040 is used to connect a communication module (not shown) to realize communication interaction between the device and other devices. The communication module can realize communication through a wired mode (such as USB, network cable, etc.) or a wireless mode (such as mobile network, WIFI, Bluetooth, etc.).

[0141] The bus 1050 includes a path that transmits information between the various components of the device (eg, the processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040).

[0142] It should be noted that, although the above device only shows the processor 1010, the memory 1020, the input / output interface 1030, the communication interface 1040 and the bus 1050, in the specific implementation process, the device may also include other components necessary for normal operation. In addition, it can be understood by those skilled in the art that the above device may also only include the components necessary for implementing the embodiments of the present specification, and does not necessarily include all the components shown in the figure.

[0143] The electronic device of the above embodiment is used to implement the corresponding model correction method in any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0144] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the model correction method described in any of the above embodiments.

[0145] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0146] The computer instructions stored in the storage medium of the above embodiment are used to enable the computer to execute the model correction method described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0147] It should be noted that the embodiments of the present application can be further described in the following manner:

[0148] A model correction method, wherein the model is an aircraft finite element model.

[0149] Methods include:

[0150] The vibration modes of the aircraft finite element model are solved to obtain the full-degree-of-freedom finite element vibration modes.

[0151] The test vibration shape is obtained, and the test vibration shape is expanded according to the finite element method to obtain the expanded vibration shape.

[0152] The aircraft finite element model is modified according to the extended vibration mode to obtain a modified model, wherein the modified model is used to perform finite element simulation on the aircraft.

[0153] Optionally, the test vibration mode is expanded according to the finite element method to obtain the expanded vibration mode, which specifically includes:

[0154] According to the finite element vibration mode of the corresponding degree of freedom of the test vibration mode, the partial transformation matrix of the corresponding degree of freedom is solved.

[0155] The partial transformation matrix is ​​solved by the following formula:

[0156]

[0157] in, represents the pseudo-inverse of the finite element vibration mode of the aircraft, ψ mj Represents the test vibration mode.

[0158] Part of the transformation matrix is ​​fitted to obtain a fitting transformation matrix.

[0159] The test vibration modes are expanded according to the fitted transformation matrix.

[0160] Optionally, fitting a part of the conversion matrix to obtain a fitting conversion matrix specifically includes:

[0161] Construct a noise vector and construct a fitted extended vibration shape based on the noise vector.

[0162] The fitting transformation matrix is ​​solved according to Bayes' theorem.

[0163] The extended mode shape is expressed by the following formula:

[0164]

[0165] in, Represents the extended vibration mode after expansion by the fitted transformation matrix. Represents the finite element mode shapes of the vehicle including the fitted degrees of freedom. Represents the fitted transformation matrix. ∈ j represents the noise vector, subject to

[0166] Optionally, solving the fitting transformation matrix according to the Bayesian theorem specifically includes:

[0167] According to the noise vector and the extended vibration shape, a Gaussian approximate function of the extended vibration shape is constructed.

[0168] The prior and posterior of the fitted extended vibration mode are solved according to Bayes' theorem.

[0169] Solve the extended vibration mode based on prior and posteriori solutions.

[0170] Among them, the Gaussian approximation function is expressed by the following formula:

[0171]

[0172] The prior is expressed by the following formula:

[0173]

[0174] in,

[0175] The posterior is expressed by the following formula:

[0176]

[0177] Optionally, after solving the fitting transformation matrix according to the Bayesian theorem, the method further includes:

[0178] The MAC value is calculated based on the extended vibration mode and the test vibration mode.

[0179] Verify the fit of the extended vibration mode based on the MAC value.

[0180] The MAC value is calculated by the following formula:

[0181]

[0182] Among them, ψ mj,fit represents the extended vibration mode. mj,obs Represents the test vibration mode.

[0183] Optionally, the aircraft finite element model is modified according to the extended vibration mode, specifically including:

[0184] The generalized eigenvalue equations of the mass matrix and stiffness matrix are constructed according to the finite element vibration modes of the aircraft.

[0185] The generalized eigenvalue equation is modified according to the extended vibration mode.

[0186] The generalized eigenvalue equations of the mass matrix and the stiffness matrix are expressed by the following formula:

[0187]

[0188] in, represents the stiffness matrix. Represents the eigenvalues ​​of the first r orders of any N×N matrix A. Represents the Nrth-order eigenvalue of any N×N matrix A. Φ aRepresents the first r-order finite element vibration mode of the aircraft. Φ b represents the finite element vibration mode of the Nrth-order aircraft. M represents the mass matrix.

[0189] Optionally, the aircraft finite element model is modified according to the extended vibration mode, specifically including:

[0190] A first matrix is ​​constructed according to the extended vibration mode, and the first matrix is ​​solved according to the finite element vibration mode of the aircraft.

[0191] The mass matrix and stiffness matrix are corrected according to the first matrix.

[0192] The first matrix is ​​represented by the following formula:

[0193]

[0194] in, represents the inverse of the first matrix. Φ FE Represents the finite element vibration mode of the N-th order aircraft.

[0195] A model correction device, wherein the model is an aircraft finite element model.

[0196] The device includes:

[0197] The model solving module is used to solve the vibration mode of the aircraft finite element model and obtain the full-degree-of-freedom finite element vibration mode.

[0198] The vibration mode expansion module is used to obtain the test vibration mode, expand the test vibration mode according to the finite element method, and obtain the extended vibration mode.

[0199] The model correction module is used to correct the finite element model of the aircraft according to the extended vibration mode to obtain a corrected model, wherein the corrected model is used to perform finite element simulation on the aircraft.

[0200] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, any of the methods described above is implemented.

[0201] A non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions are used to enable a computer to execute any of the above methods.

[0202] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present application (including the claims) is limited to these examples. In line with the concept of the present application, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of simplicity.

[0203] In addition, to simplify the description and discussion, and in order not to make the embodiments of the present application difficult to understand, the known power supply / ground connection with the integrated circuit (IC) chip and other components may or may not be shown in the provided drawings. In addition, the device can be shown in the form of a block diagram to avoid making the embodiments of the present application difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform to be implemented in the embodiments of the present application (that is, these details should be fully within the scope of understanding of those skilled in the art). In the case of elaborating specific details (e.g., circuits) to describe exemplary embodiments of the present application, it is obvious to those skilled in the art that the embodiments of the present application can be implemented without these specific details or when these specific details are changed. Therefore, these descriptions should be considered to be illustrative rather than restrictive.

[0204] Although the present application has been described in conjunction with specific embodiments of the present application, many replacements, modifications and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed.

[0205] The embodiments of the present application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the scope of protection of the present application.

Claims

1. A model correction method, wherein: The model is a finite element model of the aircraft; The method comprises: Solving the vibration mode of the finite element model of the aircraft to obtain the full-degree-of-freedom finite element vibration mode; Acquire a test vibration shape, and expand the test vibration shape according to a finite element method to obtain an expanded vibration shape; The aircraft finite element model is modified according to the extended vibration mode to obtain a modified model, wherein the modified model is used to perform finite element simulation on the aircraft.

2. The model correction method according to claim 1, wherein: The method of expanding the test vibration mode according to the finite element method to obtain the expanded vibration mode specifically includes: According to the finite element vibration mode of the degree of freedom corresponding to the test vibration mode, solving the partial transformation matrix corresponding to the degree of freedom; The partial transformation matrix is ​​solved by the following formula: in, represents the pseudo-inverse of the finite element vibration mode of the aircraft, ψ mj represents the test vibration mode; Fitting the partial conversion matrix to obtain a fitting conversion matrix; The test vibration modes are expanded according to the fitted transformation matrix.

3. The model correction method according to claim 2, wherein: The fitting of the part of the conversion matrix to obtain the fitting conversion matrix specifically includes: Constructing a noise vector, and constructing a fitted extended vibration shape according to the noise vector; Solving the fitting transformation matrix according to Bayesian theorem; The extended vibration mode is expressed by the following formula: in, represents the extended vibration shape after being expanded by the fitting transformation matrix; representing the finite element mode shapes of the aircraft including the fitted degrees of freedom; represents the fitting transformation matrix; ∈ j Represents the noise vector, subject to 4. The model correction method according to claim 3, wherein: The solving the fitting transformation matrix according to the Bayesian theorem specifically includes: Constructing a Gaussian approximation function of the extended vibration shape according to the noise vector and the extended vibration shape; Solve the prior and the posterior of the fitted extended vibration mode according to Bayes' theorem; Solving the extended vibration mode according to the priori and the posteriori; The Gaussian approximation function is expressed by the following formula: The prior is expressed by the following formula: in, The posterior is expressed by the following formula:

5. The model correction method according to claim 3, wherein: After solving the fitting transformation matrix according to the Bayesian theorem, the method further includes: Calculate the MAC value according to the extended vibration mode and the test vibration mode; Verifying the fitting of the extended vibration mode according to the MAC value; The MAC value is calculated by the following formula: Among them, ψ mj,fit represents the extended vibration mode; ψ mj,obs Represents the test vibration shape.

6. The model modification method according to claim 1, wherein: The modifying of the aircraft finite element model according to the extended vibration mode specifically includes: Constructing generalized eigenvalue equations of mass matrix and stiffness matrix according to the finite element vibration mode of the aircraft; Modifying the generalized eigenvalue equation according to the extended vibration mode; The generalized eigenvalue equations of the mass matrix and the stiffness matrix are expressed by the following formula: in, represents the stiffness matrix; Represents the eigenvalues ​​of the first r orders of any N×N matrix A; represents the Nrth-order eigenvalue of any N×N matrix A; Φ a represents the finite element vibration mode of the aircraft in the first r order; Φ b represents the finite element vibration mode of the aircraft after Nr orders; M represents the mass matrix.

7. The model modification method according to claim 6, wherein: The modifying of the aircraft finite element model according to the extended vibration mode specifically includes: Constructing a first matrix according to the extended vibration mode, and solving the first matrix according to the aircraft finite element vibration mode; Correcting the mass matrix and the stiffness matrix according to the first matrix; The first matrix is ​​represented by the following formula: in, represents the inverse of the first matrix; Φ FE Represents the finite element vibration mode of the aircraft at order N.

8. A model correction device, wherein: The model is a finite element model of the aircraft; The device comprises: A model solving module, used for solving the vibration mode of the aircraft finite element model to obtain the full-degree-of-freedom finite element vibration mode; A vibration mode expansion module is used to obtain a test vibration mode, and expand the test vibration mode according to a finite element method to obtain an expanded vibration mode; The model correction module is used to correct the aircraft finite element model according to the extended vibration mode to obtain a corrected model, wherein the corrected model is used to perform finite element simulation on the aircraft.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 7 when executing the program. 10 . A non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause a computer to execute the method according to claim 1 .

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