A strain field reconstruction method and system based on Bayesian finite element model modification

Abstract

The present invention discloses a strain field reconstruction method based on Bayesian finite element model correction, including: performing a modal test on a beam structure to obtain modal data; using the Bayesian formula to construct a posterior probability density function of a finite element model of the beam structure; selecting parameters to be corrected in the finite element model, and calculating a corrected finite element model; arranging a fiber Bragg grating sensor on the beam structure to obtain a strain response column vector, and simultaneously using the corrected finite element model to establish a finite point strain matrix and a full-field strain response matrix; solving the modal coordinates of the strain response column vector and the finite point strain matrix obtained by simulation; multiplying the modal coordinates with the full-field strain response matrix to obtain the full-field strain value under a static load condition, and realizing strain field reconstruction. The present invention combines the uncertainty finite element model correction and the strain field reconstruction method based on the modal superposition method to make the strain monitoring results of the beam structure more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of beam structure strain field reconstruction, and in particular to a strain field reconstruction method and system based on Bayesian finite element model correction. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] As an important component that bears the weight of the high-speed train, the crossbeam will be subjected to various mechanical effects for a long time during the train's operation, such as lateral and vertical loads and vibration impact, which will cause serious deformation and even cracks in the crossbeam structure, seriously endangering the safety and reliability of the train. The strain state of the crossbeam structure can reflect the structural state at this time, and can also monitor the fatigue and cracks of the structure. Therefore, it is of great significance to reconstruct the strain field of the crossbeam structure and conduct a health assessment of the structure.

[0004] The finite element modeling method is one of the best methods for structural design and analysis at present. It can effectively calculate the comprehensive information of the structure. However, due to the uncertainty in the structural production and testing process, the uncertainty of the modeling parameters, etc., the initial finite element model is usually quite different from the actual structure, which cannot fully reflect the true response of the structure and easily causes errors in a series of subsequent processing. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a strain field reconstruction method and system based on Bayesian finite element model correction. On the basis of the initial finite element model, a method combining Bayesian finite element correction and strain field reconstruction is designed, which improves the accuracy of the finite element model and the quality of the model restoring the actual structure. At the same time, the strain field reconstruction method based on modal superposition has better real-time inversion and higher accuracy.

[0006] In some embodiments, the following technical solutions are adopted:

[0007] A strain field reconstruction method based on Bayesian finite element model modification, comprising:

[0008] Conduct modal tests on the beam structure to obtain modal data;

[0009] Based on the modal data, using the Bayesian formula, constructing a posterior probability density function of the finite element model of the beam structure;

[0010] Selecting parameters of the finite element model to be corrected, using the MH-MCMC sampling method to form a Markov chain, and using the modal data to calculate a corrected finite element model;

[0011] Fiber Bragg grating sensors are arranged on the beam structure to obtain the strain response column vector, and the finite point strain matrix and the full-field strain response matrix are established using the modified finite element model.

[0012] According to the modal superposition principle, the modal coordinates are solved by the strain response column vector and the finite point strain matrix obtained by simulation; the modal coordinates are multiplied by the full-field strain response matrix to obtain the full-field strain value under static load conditions, thereby realizing strain field reconstruction.

[0013] As an optional solution, multiple modal tests are performed on the beam structure, and the modal data of the first three orders are obtained each time; the modal data at least includes the modal frequency and the modal vibration shape.

[0014] As an optional solution, the posterior probability density function of the finite element model of the beam structure is constructed, specifically:

[0015]

[0016]

[0017] When J(θ) is minimized, the posterior probability density function P(θD) is maximized;

[0018] Among them, θ is the parameter vector to be corrected, P(Dθ) is the maximum likelihood function, P(θ) is the prior distribution, D is the matrix containing the modal data information; ω is the modal frequency, is the mode shape; ω(θ) and All are output values ​​calculated by the finite element model.

[0019] As an optional solution, select the parameters of the finite element model to be modified E0 is the initial elastic modulus, and ρ0 is the initial density. The MH-MCMC sampling method is used to form a Markov chain, and the modal data is used to calculate the modified finite element model, which specifically includes:

[0020] ① Select the initial value θ0 of the parameter to be corrected;

[0021] ②Select the normal distribution q(θ * ,θ t ), according to the tth parameter value θ t , get the candidate value θ for the next moment * ;

[0022] ③According to the candidate value θ * , calculate the acceptance probability density function

[0023]

[0024] ④ Randomly generate u in the (0,1) uniform distribution:

[0025]

[0026] θ (t+1) is the (t+1)th parameter of the convergence process, θ t is the tth parameter value;

[0027] ⑤ Repeat the above process to form a convergent sequence of parameters to be corrected {θ0,θ1,...,θ n}, the final convergence value is the correction result of the finite element model parameters, and the finite element simulation is carried out using the corrected parameters.

[0028] As an optional solution, according to the modal superposition principle, the modal coordinates are solved by combining the strain response column vector with the finite point strain matrix obtained by simulation, specifically:

[0029]

[0030] in, is the strain matrix of the finite point, ε M is the strain response column vector, q n are the modal coordinates.

[0031] As an alternative, the number of sensors is greater than the order of the modes, so M ≥ n;

[0032] When M = n,

[0033] When M>n,

[0034] As an optional solution, the modal coordinates are multiplied by the full-field strain response matrix to obtain the full-field strain value under the static load condition, specifically:

[0035]

[0036] Among them, ε N is the full-field strain value under static load conditions, is the full-field strain response matrix, q n are the modal coordinates.

[0037] In other embodiments, the following technical solutions are adopted:

[0038] A strain field reconstruction system based on Bayesian finite element model correction, comprising:

[0039] Modal experiment module, used to perform modal tests on beam structures and obtain modal data;

[0040] A finite element model correction module is used to construct a posterior probability density function of the finite element model of the beam structure based on the modal data and using the Bayesian formula; select the parameters of the finite element model to be corrected, use the MH-MCMC sampling method to form a Markov chain, and use the modal data to calculate the corrected finite element model for subsequent finite element simulation;

[0041] The strain field reconstruction module is used to arrange the fiber Bragg grating sensors on the beam structure to obtain the strain response column vector, and at the same time use the modified finite element model to establish the finite point strain matrix and the full-field strain response matrix; according to the modal superposition principle, the strain response column vector and the simulated finite point strain matrix are solved for the modal coordinates; the modal coordinates are multiplied by the full-field strain response matrix to obtain the full-field strain value under the static load condition, thereby realizing strain field reconstruction.

[0042] In other embodiments, the following technical solutions are adopted:

[0043] A terminal device includes a processor and a memory, wherein the processor is used to implement various instructions; the memory is used to store multiple instructions, and the instructions are suitable for being loaded by the processor and executing the above-mentioned strain field reconstruction method based on Bayesian finite element model correction.

[0044] In other embodiments, the following technical solutions are adopted:

[0045] A computer-readable storage medium stores a plurality of instructions, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the strain field reconstruction method based on Bayesian finite element model correction.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) The present invention combines the uncertainty finite element model correction and the strain field reconstruction method based on the modal superposition method to make the strain monitoring results of the beam structure more accurate.

[0048] The uncertainty finite element model correction makes the established finite element model more practical, reduces the error between the actual response and the finite element structural response, thereby improving the accuracy of strain field reconstruction and better realizing the full-field strain response monitoring of the beam structure, which has broad application prospects.

[0049] Other features and advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of a strain field reconstruction method based on Bayesian finite element model correction in an embodiment of the present invention;

[0051] Figure 2 This is a Bayesian finite element model correction method based on MH sampling in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0053] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0054] Embodiment 1

[0055] In one or more embodiments, a strain field reconstruction method based on Bayesian finite element model modification is disclosed, combined with Figure 1 , including the following steps:

[0056] (1) Perform modal tests on the beam structure to obtain modal data;

[0057] In this embodiment, multiple modal tests are performed on the beam structure, and the modal data of the first three orders are obtained each time. The modal data includes modal frequency data and modal vibration shape data.

[0058] (2) constructing a posterior probability density function of a finite element model of the beam structure based on the modal data using the Bayesian formula;

[0059] Specifically, the Bayesian formula

[0060]

[0061] P(A|B) is the posterior probability of event A, P(B|A) is called the likelihood function or conditional probability, P(A) is the prior probability of event A, and P(B) is the marginal probability of event B. It can be seen that the independent variable of P(A|B) is A and has nothing to do with B. P(B) only plays the role of a constant regularization.

[0062] Therefore, the formula can be written as:

[0063]

[0064] The derivation process of the posterior probability density is as follows:

[0065] During the model correction process, let θ be the parameter vector to be corrected:

[0066] Y * =Y(θ)+ε (3)

[0067] ε~N(0,cov) (4)

[0068] Y * is the measured data vector, Y(θ) is the finite element calculation output vector, ε represents the test variance, and is simulated by a normal distribution N with a mean of 0 and a covariance matrix of cov.

[0069] According to the Bayesian assumption, uniform distribution is used as the prior distribution:

[0070]

[0071] Through modal testing, the frequency ω and vibration mode are obtained. If the sample data is equal, the likelihood function is:

[0072]

[0073] D is a matrix containing the modal frequencies and modal vibration shapes.

[0074] Using the linear model, the structural modal frequency ω and modal vibration shape Can be expressed as:

[0075] ω=ω(θ)+e ω (7)

[0076]

[0077] Among them, e ω , is the modal frequency error, with a mean of 0 and a variance of cov ω , The normal distribution of is a known quantity. Then:

[0078]

[0079]

[0080] Then the posterior probability density function of the parameter to be repaired is:

[0081]

[0082]

[0083] To maximize the posterior probability density function P(θD), J(θ) must be minimized.

[0084] (3) Select the parameters to be corrected in the finite element model, form a Markov chain using the MH-MCMC sampling method, and use the modal data to calculate the corrected finite element model for finite element simulation.

[0085] In this embodiment, the Markov chain is a discrete-time stochastic process with the Markov property. In this process, given the current information, the future state is only related to the current state and has nothing to do with the past state.

[0086] The Markov chain Monte Carlo method is the most popular sampling technique in Bayesian inference and is a random walk process that can be used to estimate the "target distribution". The basic idea of forming a Markov chain is as follows: First, a suitable Markov chain needs to be selected. Starting from a certain point in the space Ω, a sequence x (1) , x (2) ,... x (n) is generated using the Markov chain. When n is large enough, the expectation of x is as follows:

[0087]

[0088] m is the number of combustion samples, m < n, and the influence of the initial value needs to be considered to reduce the influence caused by improper selection of the initial value.

[0089] The process of MH sampling is as Figure 2 shown:

[0090] Select the parameters to be corrected E0 is the initial elastic modulus and ρ0 is the initial density. The process of the MH sampling method is as follows:

[0091] ① Select an initial value θ (0) .

[0092] ② According to the selected proposal distribution q(θ * , θ t ), obtain the candidate value θ * . In this embodiment, the normal distribution is selected according to experience in order to obtain the candidate value θ t at the next moment through the t-th parameter value θ * .

[0093] ③ According to the candidate value θ * , calculate the acceptance probability density function (due to the symmetry of the proposal distribution q(θ * , θ t ) = q(θ t , θ * )):

[0094]

[0095] ④ Randomly generate u in the uniform distribution of (0, 1):

[0096]

[0097] ⑤ Repeat the above process to form a convergent sequence {θ0, θ1,..., θ n}}.

[0098] (4) Arrange fiber Bragg grating sensors on the crossbeam structure to obtain a strain response column vector. At the same time, establish a finite-point strain matrix and a full-field strain response matrix using the modified finite element model;

[0099] In this embodiment, use the Abaqus finite element simulation software to apply a load to the crossbeam and establish a strain matrix of finite points and a strain matrix of the entire structure field The strain response column vector ε composed of the strains measured by FBG sensors M =[ε1 ε2 … ε M .

[0100]

[0101] In the formula, M is the number of finite nodes, and n is the selected modal order;

[0102] The strain response of all points on the crossbeam model under the action of the load is

[0103]

[0104] In the formula, N is the number of all strain points.

[0105] (5) According to the modal superposition principle, solve the modal coordinates by multiplying the strain response column vector with the simulated finite-point strain matrix; multiply the modal coordinates with the full-field strain response matrix to obtain the full-field strain value under the static load condition and realize the strain field reconstruction.

[0106] Specifically, according to the modal superposition principle, the strain response of the structure under the action of the load is the linear superposition of all strain modes:

[0107]

[0108] In the formula, q n is the modal coordinate.

[0109] When M < n, q n has infinitely many solutions. To avoid this situation, therefore, the number of sensors cannot be less than the order of the mode.

[0110] When M = n, it can be obtained by inversion:

[0111]

[0112] When M>n, multiply both sides by The following equation can be obtained:

[0113]

[0114] Further simplification yields:

[0115]

[0116] According to the modal superposition principle, the full-field strain response matrix With the modal coordinate q n Multiply them together to get the full-field strain value ε under static load conditions N :

[0117]

[0118]

[0119] Embodiment 2

[0120] In one or more embodiments, a strain field reconstruction system based on Bayesian finite element model modification is disclosed, comprising:

[0121] Modal experiment module, used to perform modal tests on beam structures and obtain modal data;

[0122] The finite element model correction module is used to construct the posterior probability density function of the finite element model of the beam structure based on the modal data and using the Bayesian formula; select the parameters to be corrected of the finite element model, use the MH-MCMC sampling method to form a Markov chain, and use the modal data to calculate the corrected finite element model for the subsequent finite element simulation;

[0123] The strain field reconstruction module is used to arrange the fiber Bragg grating sensors on the beam structure to obtain the strain response column vector, and at the same time use the modified finite element model to establish the finite point strain matrix and the full-field strain response matrix; according to the modal superposition principle, the strain response column vector and the simulated finite point strain matrix are solved for the modal coordinates; the modal coordinates are multiplied by the full-field strain response matrix to obtain the full-field strain value under the static load condition, thereby realizing strain field reconstruction.

[0124] It should be noted that the specific implementation methods of the above modules have been described in Example 1 and will not be described in detail here.

[0125] Embodiment 3

[0126] In one or more embodiments, a terminal device is disclosed, including a server, the server including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the strain field reconstruction method based on Bayesian finite element model correction in Example 1 when executing the program. For the sake of brevity, it will not be described here.

[0127] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0128] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0129] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software.

[0130] Embodiment 4

[0131] In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the strain field reconstruction method based on Bayesian finite element model correction described in Example 1.

[0132] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A strain field reconstruction method based on Bayesian finite element model modification, characterized in that: include: Conduct modal tests on the beam structure to obtain modal data; Based on the modal data, using the Bayesian formula, constructing a posterior probability density function of the finite element model of the beam structure; Selecting parameters of the finite element model to be corrected, using the MH-MCMC sampling method to form a Markov chain, and using the modal data to calculate a corrected finite element model; Fiber Bragg grating sensors are arranged on the beam structure to obtain the strain response column vector, and the finite point strain matrix and the full-field strain response matrix are established using the modified finite element model. According to the modal superposition principle, the modal coordinates are solved by combining the strain response column vector with the finite point strain matrix obtained by simulation; The modal coordinates are multiplied by the full-field strain response matrix to obtain the full-field strain value under static load conditions and realize strain field reconstruction.

2. A strain field reconstruction method based on Bayesian finite element model correction as claimed in claim 1, characterized in that: The beam structure is subjected to multiple modal tests, and the modal data of the first three orders are obtained each time; the modal data at least includes the modal frequency and the modal vibration shape.

3. The strain field reconstruction method based on Bayesian finite element model correction as claimed in claim 1, characterized in that: Construct the posterior probability density function of the finite element model of the beam structure, specifically: When J(θ) is minimized, the posterior probability density function P(θ|D) is maximized; Among them, θ is the parameter vector to be corrected, P(D|θ) is the maximum likelihood function, P(θ) is the prior distribution, D is the matrix containing the modal data information; ω is the modal frequency, is the mode shape; ω(θ) and All are output values ​​calculated by the finite element model.

4. The strain field reconstruction method based on Bayesian finite element model correction according to claim 1, characterized in that: Select the parameters of the finite element model to be modified E0 is the initial elastic modulus, ρ0 is the initial density; The Markov chain is formed by using the MH-MCMC sampling method, and the modified finite element model is calculated by using the modal data, which specifically includes: ① Select the initial value θ0 of the parameter to be corrected; ②Select the normal distribution q(θ * ,θ t ), according to the tth parameter value θ t , get the candidate value θ for the next moment * ; ③According to the candidate value θ * , calculate the acceptance probability density function ④ Randomly generate u in the (0,1) uniform distribution: θ (t+1) is the (t+1)th parameter of the convergence process, θ t is the tth parameter value; ⑤ Repeat the above process to form a convergent sequence of parameters to be corrected {θ0,θ1,...,θ n }, the final convergence value is the correction result of the finite element model parameters, and the finite element simulation is carried out using the corrected parameters.

5. The strain field reconstruction method based on Bayesian finite element model correction according to claim 1, characterized in that: According to the modal superposition principle, the modal coordinates are solved by combining the strain response column vector with the finite point strain matrix obtained by simulation, specifically: in, is the strain matrix of the finite point, ε M is the strain response column vector, q n are the modal coordinates.

6. A strain field reconstruction method based on Bayesian finite element model correction as claimed in claim 5, characterized in that: The number of sensors is greater than the order of modes, so M ≥ n; When M = n, When M>n, 7. The strain field reconstruction method based on Bayesian finite element model correction according to claim 1, characterized in that: Multiply the modal coordinates with the full-field strain response matrix to obtain the full-field strain value under static load conditions, specifically: Among them, ε N is the full-field strain value under static load conditions, is the full-field strain response matrix, q n are the modal coordinates.

8. A strain field reconstruction system based on Bayesian finite element model correction, characterized in that: include: Modal experiment module, used to perform modal tests on beam structures and obtain modal data; A finite element model correction module is used to construct a posterior probability density function of the finite element model of the beam structure based on the modal data and using the Bayesian formula; Selecting parameters of the finite element model to be corrected, using the MH-MCMC sampling method to form a Markov chain, and using the modal data to calculate a corrected finite element model for subsequent finite element simulation; The strain field reconstruction module is used to arrange the fiber Bragg grating sensor on the beam structure to obtain the strain response column vector, and at the same time use the modified finite element model to establish the finite point strain matrix and the full field strain response matrix; According to the modal superposition principle, the modal coordinates are solved by the strain response column vector and the finite point strain matrix obtained by simulation; the modal coordinates are multiplied by the full-field strain response matrix to obtain the full-field strain value under static load conditions, thereby realizing strain field reconstruction.

9. A terminal device, comprising a processor and a memory, wherein the processor is used to implement each instruction; and the memory is used to store multiple instructions, characterized in that: The instructions are suitable for being loaded by a processor and executing the strain field reconstruction method based on Bayesian finite element model correction as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a plurality of instructions, characterized in that: The instructions are suitable for being loaded by a processor of a terminal device and executing the strain field reconstruction method based on Bayesian finite element model correction as described in any one of claims 1 to 7.

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