A non-destructive evaluation method for the deterioration of the structural performance of historical buildings

Abstract

The present invention belongs to the technical field related to the evaluation of the structural performance deterioration of historical buildings, and discloses a non-destructive evaluation method for the structural performance deterioration of historical buildings. The method includes: obtaining the experimental frequencies and experimental vibration modes of historical buildings through finite element models and ambient vibration tests, obtaining the node coordinates and index numbers of the historical buildings by constructing an entity line model of the historical buildings, and then calculating the stiffness matrix and mass matrix through the node coordinates and index numbers. Based on the stiffness matrix and mass matrix, a structural dynamics equation set is established and solved to obtain the target calculation frequencies and target calculation vibration modes. Then, an objective function with the experimental frequencies, experimental vibration modes, target calculation frequencies and target calculation vibration modes as parameters is constructed, and the target Young's modulus is obtained by minimizing the objective function. According to the magnitude of the target Young's modulus, the damage degree of the corresponding calculation unit can be judged. The present application can intuitively characterize the damage degree of the beams and columns of historical buildings according to the magnitude of the Young's modulus.

Description

Technical Field

[0001] The present invention belongs to the technical field related to the evaluation of the deterioration of the structural performance of historical buildings. More specifically, it relates to a non-destructive evaluation method for the deterioration of the structural performance of historical buildings. Background Art

[0002] Historical buildings reflect the process of urban evolution over time. They are the epitome of urban history and culture, carrying on the historical context. In the current environment of urban renewal, the importance attached to historical buildings is increasing. However, due to the long construction years of historical buildings, improper use and protection, and the lack of special maintenance, the deterioration of the structural performance of historical buildings has been accelerated. Implementing special conservation measures for historical buildings to promote their reuse has become a way to effectively protect historical buildings. Throughout the entire process of historical building protection and renewal, it is necessary to detect and evaluate the structural performance of the building before renovation and renewal to support the reinforcement design, monitor the building structure during the renovation and renewal process to ensure construction safety, and conduct long-term monitoring of the building after the renovation and renewal. Once deterioration of the structural performance is detected, maintenance measures need to be taken promptly. In the prior art, regular inspections are all carried out manually. For example, the inclination of the building is measured by a total station, and the deterioration and carbonization of the building structure are evaluated by core drilling and chiseling. On the one hand, these measures cannot detect the building in a timely manner, and on the other hand, they will cause damage to the building structure. Traditional destructive testing methods (such as core drilling, chiseling, excavation, etc.) are no longer applicable to the detection of the structure of historical buildings, and existing non-destructive testing methods (such as infrared photography, radar waves, sound waves, laser point cloud scanning, etc.) also cannot quickly and comprehensively evaluate the overall disease distribution and damage condition of the building. Summary of the Invention

[0003] In view of the above-mentioned defects or improvement requirements of the prior art, the present invention provides a non-destructive evaluation method for the deterioration of the structural performance of historical buildings, which can intuitively characterize the damage degree of beams and columns of historical buildings based on the magnitude of Young's modulus.

[0004] To achieve the above object, according to one aspect of the present invention, a non-destructive evaluation method for the structural performance deterioration of historical buildings is provided. The method includes: S1: Establish a finite element model of the historical building and perform dynamic analysis on the finite element model to obtain the frequencies and vibration modes of the historical building under the first preset number of modal orders; S2: Set acceleration sensors on the floors at the intersections of the columns and beams of the historical building and conduct ambient vibration tests on the historical building to obtain the accelerations, velocities, and displacements of different position nodes of the historical building under the interference of ambient vibration; S3: Obtain the frequencies and vibration modes of the preliminary experimental modes based on the accelerations, velocities, and displacements, compare the frequencies and vibration modes of the preliminary experimental modes with the frequencies and vibration modes in step S1, and set the vibration modes and frequency errors less than 20% as the experimental frequencies and experimental vibration modes; S4: Construct a 3D solid line model of the historical building to discretize the beams and columns of the historical building into independent calculation units, and export the node coordinates and the starting and ending point index numbers of the rod elements in the 3D solid line model; S5: Construct the stiffness matrix and mass matrix of the calculation unit based on the node coordinates and index numbers; S6: Construct a structural dynamics equation set based on the stiffness matrices and mass matrices of all calculation units. The eigenvalues of the dynamics equation set are the calculated frequencies, and the eigenvectors corresponding to the eigenvalues are the calculated vibration modes; S7: Taking the experimental frequency as a reference, extract the target calculated frequency with the frequency value closest to the experimental frequency from the calculated frequencies, and extract the corresponding target calculated vibration mode; S8: Calculate the MAC value of the experimental vibration mode and the target calculated vibration mode, construct an objective function with the MAC value as a parameter and with the overall deviation between the experimental frequency and the target calculated frequency being minimized as the objective; S9: Use the particle swarm optimization algorithm to update the Young's modulus in the structural dynamics equation set to minimize the objective function, and export the corresponding target Young's modulus, and judge the damage degree of the corresponding calculation unit according to the magnitude of the target Young's modulus.

[0005] Preferably, in step S3, obtaining the frequencies and vibration modes of the preliminary experimental modes based on the accelerations, velocities, and displacements is specifically: S31: Input the accelerations, velocities, and displacements into the Artemis Model Pro software to perform enhanced frequency domain decomposition and stochastic subspace modal analysis respectively to obtain two modal analysis results; S32: Calculate the MAC value of the two modal analysis results, and select the mode with the MAC value greater than 80% to determine the final preliminary experimental mode.

[0006] Preferably, step S5 further includes removing the rows and columns corresponding to the node degrees of freedom being 0 in the stiffness matrix and mass matrix.

[0007] Preferably, step S7 further includes filling all the rows and columns where the degrees of freedom removed in step S5 are located in the target calculated vibration mode with 0.

[0008] Preferably, the structural dynamics equations in step S6 are as follows:

[0009]

[0010] where, [Ms n is the mass matrix after removing the constrained degrees of freedom of the calculation unit with index n, [Ks n is the stiffness matrix after removing the constrained degrees of freedom of the calculation unit with index n, {u n} is the displacement of the calculation unit with index n, {ü n} is the acceleration of the calculation unit with index n, {P n} is the external force applied to the calculation unit with index n.

[0011] Preferably, the formula for calculating the MAC value MAC num，exp of the experimental mode shape and the target calculated mode shape in step S8 is:

[0012]

[0013] where, is the target calculated mode shape, is the experimental mode shape, and T is the transpose.

[0014] Preferably, the objective function d is:

[0015]

[0016] where, M is the considered order, i equals 1, f num is the target calculated frequency, f exp is the experimental frequency, w f is the weight factor of the frequency term, is the weight factor of the mode shape term,

[0017] Preferably, in step S1, the finite element model is established using Abaqus software; in step S4, the 3D solid line model is established using Blender software.

[0018] Preferably, the method further includes representing the derived target Young's modulus using a color cloud map.

[0019] Preferably, step S1 further includes selecting the range of the acceleration sensor according to the frequency.

[0020] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the non-destructive evaluation method for the structural performance deterioration of historical buildings provided by the present invention mainly has the following beneficial effects:

[0021] 1. By jointly constructing an objective function for calculating the overall deviation with the experimental frequency, experimental vibration mode, calculated frequency, and calculated vibration mode of the historical building, and taking the minimum of the objective function as the optimization object, iterative optimization is performed on the established structural dynamics equation to obtain the corresponding Young's modulus. The Young's modulus can reflect the damage and deterioration degree of the material of the structural member. The change of the Young's modulus of the structural member will cause a change in the structural stiffness matrix, and this change is then reflected in the frequency and vibration mode matrices.

[0022] 2. Modal analysis is carried out in two ways: enhanced frequency domain decomposition and stochastic subspace, and then the MAC values of the two are calculated, ensuring the correctness and rationality of the preliminary experimental mode.

[0023] 3. In step S5, eliminating the rows and columns with node degrees of freedom of 0 avoids the matrix corresponding to the system of equations being a singular matrix and being unsolvable. In step S7, filling with 0 ensures that the number of eigen-solutions is consistent with the number of degrees of freedom in the system of equations.

[0024] 4. Using Abaqus software to establish a finite element model is convenient for modal analysis, and using Bleder software to establish a 3D solid line model is convenient for obtaining geometric features such as points and lines of the historical building, providing the possibility for solving the stiffness matrix and mass matrix. Description of the Drawings

[0025] Figure 1 is a step diagram of the non-destructive evaluation method for the structural performance deterioration of the historical building in the embodiment of the present application;

[0026] Figure 2 is a pre-analysis diagram of the Abaqus finite element model in the embodiment of the present application;

[0027] Figure 3 is an operational modal analysis diagram of the historical building using Artemis software in the embodiment of the present application;

[0028] Figure 4 is a result visualization diagram after parameter update through the finite element model and genetic algorithm in the embodiment of the present application. Detailed Embodiments

[0029] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0030] The present invention provides a non-destructive evaluation method for the structural performance deterioration of a historical building, as Figure 1As shown in the figure, the method includes the following steps S1 to S9.

[0031] S1: Establish a finite element model of the historical building and perform dynamic analysis on the finite element model to obtain the frequencies and vibration modes of the historical building under the first few preset order modes.

[0032] According to relevant materials such as building surveying and mapping, structural surveying, and structural exploration, pre-establish a finite element model of the historical building in Abaqus software. As Figure 2 shown, when modeling, the selection of the property parameters (Young's modulus, density, Poisson's ratio) of the structural components can refer to relevant standards or select conventional values. Perform dynamic analysis on the established finite element model to obtain a series of natural vibration frequency values and vibration modes. Select the first few (preferably the first three) modes of the overall structural torsion, offset, etc. and their corresponding frequencies. According to the range of the frequency values, select an acceleration sensor with appropriate range and accuracy. Generally, the first three-order frequencies of historical buildings are in the range of 0.01 Hz to 20 Hz, and the recommended measurement accuracy is 1000 mV / g.

[0033] S2: Set acceleration sensors on the floor at the intersections of the columns and beams of the historical building and conduct ambient vibration tests on the historical building to obtain the accelerations, velocities, and displacements of different position nodes of the historical building under the interference of ambient vibration.

[0034] To obtain the vibration data of each node of the building completely, arrange acceleration sensors at the positions where the columns and beams meet on both the inside and outside of the building. Measure the vibration responses in two directions, longitudinal and transverse, at each position. The distance between the two sensors should not be greater than two spans.

[0035] (1) Determine the positions to be arranged, use a small trowel and brush to clean the plaster layer, dust, etc. on the surface of the structure, and firmly bond the iron adsorption block to the surface of the structure with universal glue. At the same time, select a point on the inner side of the second floor and the outer side of the third floor of the building as the reference points and perform the same operations;

[0036] (2) After the universal glue is firmly bonded, shake it by hand to ensure there is no looseness, and then adsorb the acceleration sensor on the surface of the iron adsorption block along the longitudinal and transverse directions respectively (if a triaxial sensor is used, only need to firmly bond the triaxial sensor to the surface of the structure), and ensure that the sensor is firmly adsorbed;

[0037] (3) Connect the sensor and the constant current source through coaxial cables, connect the signal acquisition card to the laptop computer, start the signal acquisition software, and start signal acquisition when it is checked that the signal input is correct. The signal acquisition time should be 2000 times the period corresponding to the frequency value of interest, and the sampling rate can be set to 128 Hz;

[0038] After the data collection of each group is completed, the data collection of the next group is carried out, but it should be ensured that the position of the sensor at the reference point remains unchanged.

[0039] S3: Obtain the frequencies and mode shapes of the preliminary experimental mode based on the acceleration, velocity, and displacement, compare the frequencies and mode shapes of the preliminary experimental mode with those in step S1, and set those with mode shape and frequency errors less than 20% as the experimental frequencies and experimental mode shapes.

[0040] First, use Artemis Model Pro software for modeling. Represent the building structure in the software with nodes, lines, and surfaces. According to the number and positions of the actual measurement points, add channels through the setup - assign DOF information function. Click and hold the newly added channel with the mouse and drag it to the corresponding measurement point position on the built model to achieve the matching of the measurement point and the channel. Click the direction adjustment button to adjust the degree - of - freedom direction to be consistent with the measured direction. Import the acceleration data (or velocity, or displacement) measured in step S2 through the setup - manage measurement function, and then perform data preparation through the analysis - prepare data function. Set the filtering range to 0 to 16 Hz. Select two modal analysis methods, EFDD and SSI, and start data preparation. After the automatic data preparation is completed, view the calculation results through the analysis - estimation function, extract the peak frequencies, and obtain the corresponding mode shape data, which are recorded as the experimental frequencies and experimental mode shapes. Finally, through the analysis - validation function, automatically calculate the MAC matrix for the frequencies and mode shapes extracted by the two methods (EFDD and SSI). The MAC value should be not less than 0.8 to ensure that the frequencies and mode shapes extracted by the two methods have good consistency, and thus obtain the frequencies and mode shapes of the preliminary experimental mode, as Figure 3 shown.

[0041] Compare the frequencies and mode shapes of the preliminary experimental mode with those in step S1. Those with mode shape and frequency errors less than 20% are recorded as the first few experimental modes of the building. Extract the first few natural frequencies and the corresponding mode shapes to obtain the mode shape matrix at the measurement point positions, which are the experimental frequencies and experimental mode shapes of the historical building.

[0042] S4: Construct a 3D solid line model of the historical building to discretize the beams and columns of the historical building into independent calculation units, and export the node coordinates and the start - end point index numbers of the rod elements in the 3D solid line model.

[0043] Use Blender software to remodel the historical building structure to obtain a 3D solid line model of the historical building, and export information such as node coordinates, element numbers, and constraints. The reason for using Blender for remodeling is to obtain a 3D solid line model of the building, discretize all beams and columns of the historical building into independent calculation units respectively, which is convenient for updating these units one by one in subsequent finite element updates. In this step, first, investigate clearly the three-dimensional dimension information of the building structure, and establish a point-line model of the building structure accordingly; secondly, export all the node coordinates of the 3D solid line model and the start and end point index numbers of the bar elements. Preferably, write code in a python script to export the node coordinates of the 3D solid line model and the start and end point index numbers of the bar elements to a csv file. Secondly, box-select the nodes that need to be constrained, write code in the python script to export the index numbers of the constrained points and the degrees of freedom to be constrained, and export them to a csv file; finally, if it is necessary to analyze the response of the building under external forces, continue to box-select the points where external forces are to be applied and export the coordinates and index numbers of these points.

[0044] S5: Construct the stiffness matrix and mass matrix of the calculation unit based on the node coordinates and index numbers.

[0045] It also includes obtaining the global stiffness matrix and global mass matrix.

[0046] This embodiment can be implemented using Python. For example, in Jupyter Lab, import the required function libraries such as math, numpy, pandas, matplotlib, scipy.linalg, etc. through the pip install method.

[0047] Import the node coordinate and index number data, draw the structural point-line model, check whether there are missing calculation units in the model. If there are errors, return to step 4 to modify the 3D solid line model in Blender, re-export the data, and proceed to the next step after ensuring there are no errors.

[0048] Define the default direction of the bar element, and output the bar element length and rotation matrix.

[0049] Bar element length: For any bar element, the two end nodes are denoted as node i (coordinates (i x , i y , i z )) and node j (coordinates (j x , j y , j z ))), so the length L of the bar element is:

[0050]

[0051] Direction of bar element: Represented by a unit vector.

[0052] Unit vector in the x direction, localx unit is:

[0053] where nodes[node_j - 1] is the vector representation of node j, and nodes[node_i - 1] is the vector representation of node i.

[0054] Unit vector in the y direction, localy unit is:

[0055] localy = (node k - nodes[node_i - 1 - 1]) - [(node k - nodes[node_i - 1]) · localx unit * localx unit

[0056]

[0057] where node k is the vector representation of an arbitrary point on the X - Y plane introduced for calculation convenience.

[0058] Unit vector in the z direction, localz unit is:

[0059] localz unit = localx unit × localy unit

[0060] The rotation matrix is: TM = (localx unit , localy unit , localz unit ) T

[0061] Through the above parameters, the stiffness matrix K is:

[0062]

[0063] where A is the cross - sectional area of the calculation element, E is the Young's modulus of the calculation element, V is the Poisson's ratio, L is the length of the calculation element, G is the shear modulus, J = I p = I z + I y , I z and I y are the moments of inertia of the cross - section, and G is the shear modulus.

[0064] The global stiffness matrix Kg can be written as:

[0065] [Kg] = TM T ·[K]·TM

[0066] The mass matrix M can be expressed as a 12*12 matrix as shown below, with non-zero diagonal elements and all other elements being 0.

[0067]

[0068] Where m_point is the sum of the masses of the floor slabs of each floor of the historical building divided by the total number of nodes, that is, the mass borne by each node on average, and gamma is the linear density of the calculation unit, which is the density of the component material multiplied by the cross-sectional area, representing the mass of the component per unit length.

[0069] The global mass matrix [Mg] = [M].

[0070] This step also includes removing the rows and columns corresponding to the nodes with zero degrees of freedom in the global stiffness matrix and the global mass matrix. To remove the constrained degrees of freedom, since some immovable nodes are selected as constraints during modeling in Blender (such as all nodes on the ground floor of the first floor), the degrees of freedom of these constrained nodes are 0. In this step, find these degrees of freedom that are 0 in the global stiffness matrix and the global mass matrix, delete the rows and columns where they are located, and the new matrix composed of the remaining elements is the mass matrix [Ms] and the stiffness matrix [Ks] after removing the constrained degrees of freedom.

[0071] S6: Construct a structural dynamics equation system based on the stiffness matrix [Ks] and the mass matrix [Ms] of all calculation units. The eigenvalues of the dynamics equation system are the calculated frequencies, and the eigenvectors corresponding to the eigenvalues are the calculated vibration modes.

[0072] The structural dynamics equation system is:

[0073]

[0074] Where [Ms n is the mass matrix of the calculation unit with index n after removing the constrained degrees of freedom, [Ks n is the stiffness matrix of the calculation unit with index n after removing the constrained degrees of freedom, {u n} is the displacement of the calculation unit with index n, {ü n} is the acceleration of the calculation unit with index n, and {P n} is the external force acting on the calculation unit with index n.

[0075] Furthermore, based on the above equations, the eigenvalues and eigenvectors of the equations can be solved. The eigenvalues are the calculated frequencies, and the eigenvectors corresponding to the eigenvalues are the calculated vibration modes. The above equations can be algorithmically analyzed using Python.

[0076] S7: Based on the experimental frequency, extract the target calculated frequency with the frequency value closest to the experimental frequency from the calculated frequencies, and extract the corresponding target calculated vibration mode.

[0077] Based on the above experimental frequency, search for the frequency value closest to the experimental frequency among the calculated frequencies, which is the target calculated frequency, and extract the corresponding mode matrix, which is the target calculated vibration mode. For example, if the first three experimental frequencies are K1 = 1.973, K2 = 3.535, and K3 = 8.005 respectively, then find the values closest to these three values (the smallest absolute difference) among the eigenvalues obtained in the previous step, and the corresponding eigenvectors are the mode matrices to be extracted.

[0078] This step also includes filling all rows and columns where the degrees of freedom removed in step S5 are located in the target calculated vibration mode with 0.

[0079] S8: Calculate the MAC value between the experimental vibration mode and the target calculated vibration mode, and construct an objective function with the MAC value as a parameter and the overall deviation between the experimental frequency and the target calculated frequency being minimized as the goal.

[0080] Calculate the MAC value MAC between the experimental vibration mode and the target calculated vibration mode num，exp The calculation formula is:

[0081]

[0082] Among them, is the target calculated vibration mode, is the experimental vibration mode, and T is the transpose.

[0083] The objective function d is:

[0084]

[0085] Among them, M is the considered order, i is equal to 1, f num is the target calculated frequency, f exp is the experimental frequency, w f is the weight factor of the frequency term, is the weight factor of the mode term,

[0086] S9: The Young's modulus in the structural dynamics equations is updated using the particle swarm optimization algorithm to minimize the objective function, and the corresponding target Young's modulus is derived. The damage degree of the corresponding calculation unit is judged according to the magnitude of the target Young's modulus.

[0087] The Young's modulus in the structural dynamics equations is updated using the particle swarm optimization (PSO) algorithm to minimize the objective function, and other parameters such as density, Poisson's ratio, cross-sectional area, and moment of inertia of the cross-section are kept unchanged during the update process. The maximum velocity in the PSO algorithm is set to 6, the weight coefficients are 0.9 and 0.2, the learning factors c1 and c2 are both 2, the population size is set to 20, and the number of iterations is 20 times (the population size and the number of iterations can be appropriately increased. Generally, the population size is not greater than 50, and the number of iterations is not greater than 500). Iterative calculations are performed to obtain the target Young's modulus.

[0088] Furthermore, it also includes representing the derived target Young's modulus using a color cloud map, such as Figure 4 shown. For calculation units of the same type, the smaller the Young's modulus value, the more serious the damage or material property degradation of the calculation unit. On the contrary, the larger the Young's modulus, the less damage or smaller damage exists in the component, and the lighter the material degradation. In actual operation, the critical threshold of the Young's modulus can be set according to needs.

[0089] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A non-destructive evaluation method for the deterioration of the structural performance of historical buildings, characterized in that, The method includes: S1: Establish a finite element model of the historical building and perform dynamic analysis on the finite element model to obtain the frequencies and vibration modes of the historical building under the first preset number of modal orders; S2: Set acceleration sensors on the floor at the intersections of the columns and beams of the historical building and conduct ambient vibration tests on the historical building to obtain the acceleration, velocity, and displacement at different position nodes of the historical building under the interference of ambient vibration; S3: Obtain the frequencies and vibration modes of the preliminary experimental mode based on the acceleration, velocity, and displacement, compare the frequencies and vibration modes of the preliminary experimental mode with those in step S1, and set those with a vibration mode and frequency error less than 20% as the experimental frequencies and experimental vibration modes; S4: Construct a 3D solid line model of the historical building to discretize the beams and columns of the historical building into independent calculation units, and export the node coordinates and the starting and ending point index numbers of the rod elements in the 3D solid line model; S5: Construct the stiffness matrix and mass matrix of the calculation unit based on the node coordinates and index numbers; S6: Construct a structural dynamics equation set based on the stiffness matrices and mass matrices of all calculation units. The eigenvalues of the dynamics equation set are the calculated frequencies, and the eigenvectors corresponding to the eigenvalues are the calculated vibration modes; S7: Based on the experimental frequencies, extract the target calculated frequencies with the frequency values closest to the experimental frequencies from the calculated frequencies, and extract the corresponding target calculated vibration modes; S8: Calculate the MAC value of the experimental vibration mode and the target calculated vibration mode, construct an objective function with the MAC value as a parameter and with the overall deviation between the experimental frequency and the target calculated frequency being minimized as the goal; S9: Use the particle swarm optimization algorithm to update the Young's modulus in the structural dynamics equation set to minimize the objective function, export the corresponding target Young's modulus, and judge the damage degree of the corresponding calculation unit according to the magnitude of the target Young's modulus.

2. The method according to claim 1, characterized in that, In step S3, obtaining the frequencies and vibration modes of the preliminary experimental mode based on the acceleration, velocity, and displacement specifically includes: S31: Input the acceleration, velocity, and displacement into the Artemis Model Pro software to perform enhanced frequency domain decomposition and stochastic subspace modal analysis respectively to obtain two modal analysis results; S32: Calculate the MAC value for the two modal analysis results, and select the mode with a MAC value greater than 80% to determine the final preliminary experimental mode.

3. The method according to claim 1, wherein Step S5 also includes calculating the global mass matrix and global stiffness matrix, and step S5 also includes removing the rows and columns corresponding to the node degrees of freedom being 0 in the global stiffness matrix and global mass matrix.

4. The method according to claim 3, wherein Step S7 also includes filling all the rows and columns corresponding to the degrees of freedom removed in step S5 in the target calculated vibration mode with 0.

5. The method according to claim 1, characterized in that The structural dynamics equation set in step S6 is: Among them, [Ms n is the mass matrix of the calculation unit with index n after removing the constrained degrees of freedom, [Ks n is the stiffness matrix of the calculation unit with index n after removing the constrained degrees of freedom, {u n} is the displacement of the calculation unit with index n, is the acceleration of the calculation unit with index n, {P n} is the external force acting on the calculation unit with index n.

6. The method according to claim 1, characterized in that In step S8, the MAC value MAC of the experimental mode shape and the target calculated mode shape is obtained num，exp The calculation formula is as follows: Among them, is the target calculated vibration mode, is the experimental vibration mode, and T is the transpose.

7. The method according to claim 6, wherein The objective function d is: where M is the order considered, i equals 1, f num is the target calculation frequency, f exp is the experimental frequency, w f is the weight factor of the frequency term, is the weight factor of the mode shape term, 8. The method according to claim 1, wherein In step S1, the Abaqus software is used to establish the finite element model; in step S4, the Blender software is used to establish the 3D solid line model.

9. The method according to claim 1, wherein The method also includes representing the exported target Young's modulus using a color cloud map.

10. The method according to claim 1, characterized in that, Step S1 also includes selecting the range of the acceleration sensor according to the frequency.

Images