Structural damage identification method, system and equipment based on strain generalized flexibility matrix
Through the structural damage recognition method based on the strain generalized flexibility matrix, the problems of traditional methods being insensitive to small damage and weak anti-noise ability are solved, and the accurate identification of the position and degree of structural damage is achieved, and the recognition accuracy and anti-noise performance are improved.
Patent Information
- Application Number
- CN202411862064.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-17
- Publication Date
- 2025-05-02
AI Technical Summary
The traditional generalized flexibility matrix damage recognition method is insensitive to small damage, has weak anti-noise ability, and cannot recognize large damage conditions, and the recognition results may have negative values, limiting the promotion and application of the method.
The structural damage recognition method based on the strain generalized flexibility matrix is adopted. By establishing a finite element model of a healthy structure, the frequency, displacement vibration mode and strain vibration mode after the damage are measured, the strain generalized flexibility matrix is constructed, the change amount under the damage state is calculated, the sensitivity equation is constructed, and it is converted into a constrained optimization problem for solving, and the damage coefficients satisfying the physical meaning are obtained.
This method can simultaneously identify the damage location and damage degree of the structure, improve the sensitivity to small damage, enhance the anti-noise performance, avoid the occurrence of negative damage coefficients, and have higher recognition accuracy.
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Figure CN119918332A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of structural health monitoring, and in particular to a structural damage identification method, system and equipment based on a strain generalized flexibility matrix. Background Art
[0002] In recent years, with the increasing complexity and size of engineering structures, rod structures have been increasingly used in various important buildings. However, during long-term service, factors such as material aging, environmental erosion, and load changes may cause the mechanical properties of rods to deteriorate, which in turn leads to problems with the overall safety of the structure. Especially in large-scale space trusses and grid structures, the failure of any single rod may have a serious impact on the stability and safety of the overall structure. Therefore, studying how to effectively identify and evaluate the damage of rod structures during service has become an important topic to ensure structural safety.
[0003] Traditional structural health monitoring methods, such as visual inspection and local nondestructive testing techniques (ultrasound, X-ray, etc.), can identify structural damage to a certain extent, but they usually have limitations such as strong locality, long time consumption, low efficiency, and high dependence on the environment. In order to solve these problems, vibration-based structural damage identification methods have received widespread attention in recent years. This method can identify global structural damage by monitoring the dynamic response data of the structure and combining modern signal processing technology and structural dynamics theory.
[0004] Among these vibration-based damage identification methods, structural dynamic fingerprint indicators have been studied in depth as an important means. These indicators can reflect the changes in the dynamic characteristics of the structure and are thus used to evaluate the health status of the structure. Among them, the damage identification method based on the generalized flexibility matrix proposed by Li Jing has shown good potential in practical applications because it only requires low-order modal data of the structure. The core idea of the generalized flexibility matrix method is to capture the changes in structural stiffness through the changes in the generalized flexibility matrix, thereby identifying the location and degree of structural damage. Since this method relies on the low-order modal data of the structure, which is easier to measure and less susceptible to noise than high-order modal data, this method has strong applicability and reliability in engineering practice. However, although vibration-based damage identification methods have made significant progress in theoretical and experimental research, they still face some problems in practical engineering applications. The traditional generalized flexibility matrix damage identification method is insensitive to small damage, has weak anti-noise ability, and cannot identify large damage conditions. What is more serious is that the identification results will be negative, which seriously restricts the promotion and application of this method. Summary of the invention
[0005] In view of the above-mentioned problems, the present invention aims to provide a structural damage identification method, system and equipment based on strain generalized flexibility matrix, defines a strain-based generalized flexibility matrix, constructs a damage identification equation based on the strain generalized flexibility matrix using a sensitivity analysis method, converts the damage identification equation into a constrained optimization problem for solution, obtains a damage coefficient that satisfies the physical meaning, and can simultaneously identify the location and degree of structural damage.
[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:
[0007] The structural damage identification method based on strain generalized flexibility matrix includes the following steps:
[0008] S1: Establish a finite element model of the healthy structure and extract the corresponding unit stiffness matrix and unit mass matrix as well as the frequency, displacement mode shape and strain mode shape;
[0009] S2: Carry out dynamic testing on the damaged structure to measure the corresponding frequency, displacement mode and strain mode;
[0010] S3: construct the strain generalized flexibility matrix;
[0011] S4: Calculate the change of the generalized flexibility matrix of the structural strain under the damage state;
[0012] S5: Based on the change of the generalized flexibility matrix of structural strain under the damage state, the structural damage identification sensitivity equation based on the generalized flexibility matrix of strain is constructed;
[0013] S6: Construct a constrained structural damage identification objective function, use a constrained optimization method to solve the objective function, and obtain the damage coefficient value;
[0014] S7: Determine whether the convergence condition is met. If the convergence condition is met, output the recognition result. If the convergence condition is not met, repeat the above step S6.
[0015] Furthermore, the basic form of the strain generalized flexibility matrix described in step S3 is:
[0016] f ε =F ε (MF) l
[0017] Among them, f ε represents the strain generalized flexibility matrix; l represents the order of the strain generalized flexibility matrix; F ε =TF, T represents the relationship between unit strain and displacement in the global coordinate system; F is related to the stiffness matrix K of the structure and is obtained by inverting the stiffness matrix K.
[0018] The strain generalized flexibility matrix is approximately expressed using the measured low-order strain modes and displacement modes.
[0019]
[0020] Where m is the modal order obtained from the actual test, usually m is less than or equal to the degree of freedom of the structure; Ω is the diagonal matrix composed of squared frequencies; φ is the displacement mode shape normalized with respect to the mass matrix; φ ε are the strain mode shapes normalized with respect to the mass matrix.
[0021] Furthermore, the change Δf of the generalized flexibility matrix of the structural strain under the damage state in step S4 is ε for
[0022]
[0023] in, is the generalized flexibility matrix of structural strain under damage state; is the generalized flexibility matrix of structural strain in the healthy state; is the i-th order post-damage strain mode shape; is the i-th order pre-damage strain mode; φ id is the displacement mode shape after damage of the ith order; φ iu is the i-th order pre-damage displacement mode, ω d is the frequency of the damaged structure; ω u is the frequency of the structure in a healthy state, the subscript d indicates the structural damage state, and the subscript u indicates the healthy state.
[0024] Furthermore, the structural damage identification sensitivity equation based on the strain generalized flexibility matrix in step S5 is expressed as
[0025]
[0026] In the formula, a j is the damage factor of the jth member, N represents the number of members in the structure; is the structural strain flexibility matrix in the healthy state; F u is the structural displacement flexibility matrix under healthy state, and the structural strain generalized flexibility matrix under healthy state Included and F u ; is the stiffness matrix of the structure in the i-th healthy state under global coordinates.
[0027] Furthermore, the objective function of constrained structural damage identification in step S6 is
[0028] minJ(a)=D||Δf ε -G(a)||2
[0029] Where D is the amplification factor; Δf ε represents the actual measured value of the change in the generalized flexibility matrix, Theoretical expression representing the change of the generalized flexibility matrix.
[0030] Furthermore, in step S6, a sequential quadratic programming algorithm is used to solve the structural damage identification objective function.
[0031] Furthermore, the convergence condition in step S7 is
[0032]
[0033] Among them, a n represents the damage coefficient during the nth iteration, and s is the threshold of the convergence condition.
[0034] Furthermore, the present invention also includes a structural damage identification system based on a strain generalized flexibility matrix, the structural damage identification system including a healthy structure finite element model building module, a structural damage data acquisition module, a strain generalized flexibility matrix building module, and an optimization objective function solving module;
[0035] The healthy structure finite element model building module is used to build the finite element model of the healthy structure and extract the corresponding unit stiffness matrix and unit mass matrix and frequency, displacement mode shape and strain mode shape;
[0036] The structural damage data acquisition module is used to measure the frequency, displacement mode and strain mode corresponding to the structural damage;
[0037] The strain generalized flexibility matrix construction module is used to construct the strain generalized flexibility matrix;
[0038] The optimization objective function solving module calculates the change of the structural strain generalized flexibility matrix under the damage state based on the strain generalized flexibility matrix, and constructs the structural damage identification sensitivity equation and the optimization method to solve the objective function for solution;
[0039] Among them, the healthy structure finite element model construction module, the structural damage data acquisition module, the strain generalized flexibility matrix construction module, and the optimization objective function solution module are all implemented based on the structural damage identification method described above.
[0040] Furthermore, the present invention also includes an electronic device, which includes at least one processor; and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute the structural damage identification method as described above.
[0041] The beneficial effects of the present invention are:
[0042] 1. The present invention discloses a structural damage identification method based on a strain generalized flexibility matrix, taking the elastic modulus reduction rate of the rod as the damage coefficient, taking the frequency, displacement vibration mode and strain mode after structural damage as the observation data, adopting the conversion relationship between strain and displacement, defining the strain generalized flexibility matrix, and deriving the sensitivity equation of the change of the strain generalized flexibility matrix to the damage coefficient before and after structural damage. After finite term truncation, a damage identification equation based on the strain generalized flexibility matrix is established, and considering the physical meaning of the damage coefficient, a constrained optimization algorithm is used to solve the above sensitivity equation. The strain data used in the present invention is easy to measure and sensitive to damage in practical applications. Compared with traditional vibration modes, smaller damage conditions can be identified, and negative damage coefficients will not appear, which meets physical requirements; the identification accuracy is higher and it has better anti-noise performance.
[0043] 2. Compared with the generalized flexibility matrix in the prior art, the strain generalized flexibility matrix in the present invention is more sensitive to structural damage and helps to identify small damage conditions of the structure. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] Figure 1 It is a flow chart of the structural damage identification method based on strain generalized flexibility matrix in the present invention.
[0045] Figure 2 It is a schematic diagram of the cantilever beam structure in the simulation experiment of the present invention.
[0046] Figure 3 It is a schematic diagram of the sensor arrangement and grid node division method when obtaining structural damage data in the simulation experiment of the present invention.
[0047] Figure 4 It is the first three-order displacement vibration mode diagram of the structure in the simulation experiment of the present invention.
[0048] Figure 5 This is the acceleration response signal diagram of node 1 in the simulation experiment of the present invention.
[0049] Figure 6 This is the identification result of a single damage condition in the simulation experiment of the present invention.
[0050] Figure 7 This is the result of identifying multiple damage conditions in the simulation experiment of the present invention. DETAILED DESCRIPTION
[0051] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.
[0052] Embodiment 1:
[0053] Embodiment 1 provides a structural damage identification method based on strain generalized flexibility matrix, as shown in the attached Figure 1 As shown, the following steps are included:
[0054] S1: Establish a finite element model of the healthy structure and extract the corresponding unit stiffness matrix and unit mass matrix as well as the frequency, displacement mode shape and strain mode shape;
[0055] Specifically, establishing a finite element model of a healthy structure is an existing technology. According to different structural forms, corresponding finite element models are established. The specific process is not described in detail in this invention. The finite element model correction method is used to correct the parameters of the established structural finite element model so that the frequency and vibration mode output by the finite element model and the frequency and vibration mode error of the actual structure measurement are less than 3%.
[0056] The unit stiffness matrix and unit mass matrix of the structural finite element model are extracted, and the mass matrix M and stiffness matrix K can be formed after considering the constraints.
[0057] Further, step S2: carry out dynamic testing on the damaged structure to measure the corresponding frequency, displacement vibration mode and strain vibration mode. Strain sensors and acceleration sensors are placed in the actual damaged structure. The structure is vibrated by environmental excitation. The collected vibration signal is filtered by a low-pass filter. Finally, the random subspace method is used to analyze the filtered vibration signal to obtain the frequency, displacement vibration mode and strain vibration mode of the damaged structure. It should be noted that the displacement vibration mode and strain vibration mode need to be normalized with respect to the mass matrix. Taking the normalization of the displacement vibration mode as an example,
[0058]
[0059] in, represents the displacement mode shape before normalization with respect to mass, and φ represents the displacement mode shape before normalization with respect to mass.
[0060] Further, step S3: constructing a strain generalized flexibility matrix;
[0061] Specifically, the basic form of the strain generalized flexibility matrix is
[0062] f ε =F ε (MF) l
[0063] Among them, f ε represents the strain generalized flexibility matrix, l represents the order of the strain generalized flexibility matrix, and in the present invention, l=1, that is, f ε =F ε MF; F ε=TF, T represents the relationship between unit strain and displacement in the global coordinate system; F is related to the stiffness matrix K of the structure, which is obtained by inverting the stiffness matrix K.
[0064] The strain generalized flexibility matrix is approximately expressed using the measured low-order strain modes and displacement modes.
[0065]
[0066] Where m is the modal order obtained from the actual test, usually m is less than or equal to the degree of freedom of the structure; Ω is the diagonal matrix composed of square frequencies; φ is the displacement mode shape normalized with respect to the mass matrix, φ ε are the strain mode shapes normalized with respect to the mass matrix.
[0067] Further, step S4: calculate the change of the generalized flexibility matrix of the structural strain under the damage state; specifically, the change Δf of the generalized flexibility matrix of the structural strain under the damage state ε for
[0068]
[0069] in, is the generalized flexibility matrix of structural strain under damage state; is the generalized flexibility matrix of structural strain in the healthy state; is the i-th order post-damage strain mode shape; is the strain mode shape before damage (healthy state) of the i-th order; φ id is the displacement mode shape after damage of the ith order; φ iu is the displacement mode shape before damage (healthy state) of the i-th order, ω d is the frequency of the damaged structure; ω u is the frequency of the structure in a healthy state, the subscript d indicates the structural damage state, and the subscript u indicates the healthy state.
[0070] Further, step S5: based on the change of the generalized flexibility matrix of the structural strain under the damage state, constructing a structural damage identification sensitivity equation based on the generalized flexibility matrix of the strain;
[0071] Specifically, the structural damage identification sensitivity equation based on the strain generalized flexibility matrix is expressed as
[0072]
[0073] In the formula, a j is the damage factor of the jth member, N represents the number of members in the structure; is the structural strain flexibility matrix in the healthy state; F u is the structural displacement flexibility matrix under healthy state, and the structural strain generalized flexibility matrix under healthy state Included and F u ; is the stiffness matrix of the structure in the i-th healthy state under global coordinates.
[0074] Further, step S6: construct a constrained structural damage identification objective function, and use a constrained optimization method to solve the objective function to obtain a damage coefficient value;
[0075] Specifically, the objective function of constrained structural damage identification is:
[0076] minJ(a)=D||Δf ε -G(a)||2
[0077] Where D is the amplification factor. Since the flexibility matrix values are very small, the accuracy of the optimization result can be adjusted by D; Δf ε represents the actual measured value of the change in the generalized flexibility matrix, Theoretical expression representing the change of the generalized flexibility matrix.
[0078] The optimization problem is solved using a sequential quadratic programming algorithm, which can be implemented in MATLAB using the fmincon function.
[0079] Further, step S7: determine whether the convergence condition is met, if the convergence condition is met, output the recognition result, if not, repeat the above step S6.
[0080] Specifically, the convergence condition is
[0081]
[0082] Among them, a n represents the damage coefficient in the nth iteration process, s is the threshold of the convergence condition, specifically a very small positive vector. In the present invention, s=(1,1,1,1,1,1,1,1,1,1,1)×10 -5 .
[0083] Simulation experiment:
[0084] This simulation experiment uses the following Figure 2 The cantilever beam structure shown is simulated.
[0085] The finite element method is used to establish the mass and stiffness matrix of the beam. The total number of elements is 10, and the element stiffness matrix K e and the element mass matrix M e They are
[0086]
[0087] Among them, E is the elastic modulus, I is the section inertia moment, ρ is the mass per unit length, and L is the length of the beam. After considering the constraints, the mass matrix M and the stiffness matrix K can be formed. The Rayleigh damping ratio is used to describe the structural damping C = aM + βK, a = 0.001, β = 0.001.
[0088] This simulation experiment sets up two damage conditions: single damage condition, the elastic modulus of unit 8 is reduced by 5%; multiple damage condition, the elastic modulus of unit 2 is reduced by 25%, and the elastic modulus of unit 4 is reduced by 35%. The damage of the structure does not consider the change of mass, only the reduction of elastic modulus.
[0089] Further, according to the attached Figure 3 The sensor arrangement and grid node division method shown in the figure are used to arrange strain sensors and acceleration sensors on the actual damaged structure. The structural vibration is stimulated by environmental excitation. Figure 4 The acceleration time history curve at node 1 is shown. The collected vibration time history signal is filtered using a low-pass filter. Finally, the random subspace method is used to analyze the filtered vibration signal to obtain the structural frequency before and after damage (as shown in Table 1 below), displacement mode shape and strain mode shape. Figure 5 The displacement mode shapes for the healthy state are shown.
[0090] Table 1 Structural natural vibration frequency under various working conditions
[0091]
[0092] The damage identification results of single damage and multiple damage conditions are shown in the attached figure. Figure 6 and attached Figure 7 As shown. The strain generalized flexibility matrix method and the generalized flexibility matrix method are used to identify the damaged unit 8 of the single damage condition, and the identification errors are 1% and -6% respectively. The strain generalized flexibility matrix method and the generalized flexibility matrix method are used to identify the damaged unit 2 of multiple damage conditions, and the identification errors are 9.6% and -40.0% respectively; the identification errors of the damaged unit 4 of multiple damage conditions are 17.1% and -22.57% respectively. This shows that the identification result of the single damage condition is better than that of multiple damage conditions, and the identification effect of the strain generalized flexibility matrix method is much better than that of the generalized flexibility matrix method. In addition, from Figure 6 and Figure 7 It can be seen that the generalized flexibility matrix method will produce negative identification results, while the strain generalized flexibility matrix method in the present invention will not have negative results and can identify a greater degree of damage.
[0093] Embodiment 2:
[0094] Embodiment 2 provides a structural damage identification system based on strain generalized flexibility matrix, the structural damage identification system comprising a healthy structure finite element model building module, a structural damage data acquisition module, a strain generalized flexibility matrix building module, and an optimization objective function solving module;
[0095] The healthy structure finite element model building module is used to build the finite element model of the healthy structure and extract the corresponding unit stiffness matrix and unit mass matrix and frequency, displacement mode shape and strain mode shape;
[0096] The structural damage data acquisition module is used to measure the frequency, displacement mode and strain mode corresponding to the structural damage;
[0097] The strain generalized flexibility matrix construction module is used to construct the strain generalized flexibility matrix;
[0098] The optimization objective function solving module calculates the change of the structural strain generalized flexibility matrix under the damage state based on the strain generalized flexibility matrix, and constructs the structural damage identification sensitivity equation and the optimization method to solve the objective function for solution.
[0099] It should be noted that the healthy structure finite element model building module, the structural damage data acquisition module, the strain generalized flexibility matrix building module, and the optimization objective function solving module in this embodiment are all implemented based on the structural damage identification method in the first embodiment.
[0100] Embodiment three:
[0101] Embodiment 3 provides an electronic device, comprising at least one processor; and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute the structural damage identification method described in Embodiment 1.
[0102] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.
Claims
1. A structural damage identification method based on strain generalized flexibility matrix, characterized in that: The following steps are included: S1: Establish a finite element model of the healthy structure and extract the corresponding element stiffness matrix, element mass matrix, frequency, displacement mode shape and strain mode shape; S2: Carry out dynamic testing on the damaged structure to measure the corresponding frequency, displacement mode and strain mode; S3: construct the strain generalized flexibility matrix; S4: Calculate the change of the generalized flexibility matrix of the structural strain under the damage state; S5: Based on the change of the generalized flexibility matrix of structural strain under the damage state, the structural damage identification sensitivity equation based on the generalized flexibility matrix of strain is constructed; S6: Construct a constrained structural damage identification objective function, use a constrained optimization method to solve the objective function, and obtain the damage coefficient value; S7: Determine whether the convergence condition is met. If the convergence condition is met, output the recognition result. If the convergence condition is not met, repeat the above step S6.
2. The structural damage identification method based on strain generalized flexibility matrix according to claim 1 is characterized in that: The basic form of the strain generalized flexibility matrix described in step S3 is favorite ε =F ε (MF) l Among them, f ε represents the strain generalized flexibility matrix, l represents the order of the strain generalized flexibility matrix, F ε =TF, T represents the relationship between unit strain and displacement in the global coordinate system; F is related to the stiffness matrix K of the structure and is obtained by inverting the stiffness matrix K; The strain generalized flexibility matrix is approximately expressed using the measured low-order strain modes and displacement modes. Where m is the modal order obtained from the actual test, usually m is less than or equal to the degree of freedom of the structure; Ω is the diagonal matrix composed of square frequencies; φ is the displacement mode shape normalized with respect to the mass matrix, φ ε are the strain mode shapes normalized with respect to the mass matrix.
3. The structural damage identification method based on strain generalized flexibility matrix according to claim 2 is characterized in that: The change Δf of the generalized flexibility matrix of the structural strain under the damage state in step S4 ε for in, is the generalized flexibility matrix of structural strain under damage state; is the generalized flexibility matrix of structural strain in the healthy state; is the i-th order post-damage strain mode shape; is the i-th order pre-damage strain mode; φ id is the displacement mode shape after damage of the ith order; φ iu is the i-th order pre-damage displacement mode, ω d is the frequency of the damaged structure; ω u is the frequency of the structure in a healthy state; the subscript d indicates the damaged state of the structure, and the subscript u indicates the healthy state.
4. The structural damage identification method based on strain generalized flexibility matrix according to claim 3 is characterized by: The structural damage identification sensitivity equation based on the strain generalized flexibility matrix in step S5 is expressed as In the formula, a j is the damage factor of the jth member, N represents the number of members in the structure; is the structural strain flexibility matrix in the healthy state; F u is the structural displacement flexibility matrix under healthy state, and the structural strain generalized flexibility matrix under healthy state Included and F u ; is the stiffness matrix of the structure in the i-th healthy state under global coordinates.
5. The structural damage identification method based on strain generalized flexibility matrix according to claim 4 is characterized in that: The objective function of constrained structural damage identification in step S6 is: min J(a)=D||Δf ε -G(a)||2 Where D is the amplification factor; Δf ε represents the actual measured value of the change in the generalized flexibility matrix, Theoretical expression representing the change of the generalized flexibility matrix.
6. The structural damage identification method based on strain generalized flexibility matrix according to claim 5 is characterized by: In step S6, a sequential quadratic programming algorithm is used to solve the structural damage identification objective function.
7. The structural damage identification method based on strain generalized flexibility matrix according to claim 6 is characterized by: The convergence condition in step S7 is Among them, a n represents the damage coefficient during the nth iteration, and s is the threshold of the convergence condition.
8. Structural damage identification system based on strain generalized flexibility matrix, characterized by: It includes healthy structure finite element model building module, structural damage data acquisition module, strain generalized flexibility matrix building module, and optimization objective function solving module; The healthy structure finite element model building module is used to build the finite element model of the healthy structure and extract the corresponding unit stiffness matrix and unit mass matrix and frequency, displacement mode shape and strain mode shape; The structural damage data acquisition module is used to measure the frequency, displacement mode and strain mode corresponding to the structural damage; The strain generalized flexibility matrix construction module is used to construct the strain generalized flexibility matrix; The optimization objective function solving module calculates the change of the structural strain generalized flexibility matrix under the damage state based on the strain generalized flexibility matrix, and constructs the structural damage identification sensitivity equation and the optimization method to solve the objective function for solution; Among them, the healthy structure finite element model building module, the structural damage data acquisition module, the strain generalized flexibility matrix building module, and the optimization objective function solving module are all implemented based on the structural damage identification method in any one of claims 1-7.
9. An electronic device, characterized in that: It comprises at least one processor; and a memory in communication connection with the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute the structural damage identification method described in any one of claims 1 to 7.