CN109975136B - Steel frame structure damage identification method based on wavelet packet analysis - Google Patents
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Abstract
The invention discloses a steel frame structure damage identification method based on wavelet packet analysis, which comprises the following steps of firstly, acquiring acceleration responses of measurement points of a structural model before and after the steel frame structure is damaged under the same impact condition, and arranging the acceleration responses into an initial sample set according to the geometric positions of frame beams and columns: and finally, carrying out wavelet packet transformation on the vibration response of each measuring point, further obtaining a wavelet packet energy characteristic vector, identifying by using the damage identification index EVSDR provided by the invention, judging the occurrence of structural damage and the position of the damage according to a peak value, and representing the structural damage and the position of the damage by using a view so as to realize visualization. The method can be used for diagnosing the occurrence of the damage of the steel frame structure, determining the occurrence position of the damage and evaluating the change of the damage degree after the damage at the same position is accumulated; the method improves the damage identification capability by utilizing the signal identification microscopic characteristic of the wavelet packet, is simple, and is suitable for structural damage identification and health monitoring of the steel frame structure.
Description
Technical Field
The invention relates to the technical field, in particular to a steel frame structure damage identification method based on wavelet packet analysis.
Background
As historical progress has continued forward, a large number of buildings built early have been or will be near their design life. In the service period of the steel structure for decades or even longer, the accumulated damage of the structure is aggravated due to the coupling effect of adverse factors such as environmental erosion, material aging, long-term effect of dynamic and static loads, fatigue effect, mutation effect and the like, and the sudden damage of the whole structure can be possibly caused. In 1979, the roof suddenly collapses due to fatigue failure of a part of high-strength bolts under the action of long-term wind load in the kenpa gym in the United states. In 2004, the initial cracks at the joint of the circular steel structure strut and the ceiling of the 2E airport waiting hall in Paris, are damaged and accumulated continuously under the long-term action of wind load, so that the joint is suddenly broken, and the ceiling of the waiting hall collapses. Russian cumosovon swimming pools broke due to long-term corrosion of the metal frame, resulting in collapse of the ceiling. Steel frame structures are one of the common structural forms in steel construction. In order to ensure the normal operation of the steel frame structure during service, avoid the sudden damage of the structure and avoid the potential safety hazard of the structure, the real-time online health monitoring of the steel frame structure is necessary. The structural damage identification method is the core of health monitoring, and refers to detecting and evaluating a structure to determine whether the structure is damaged, and further judging the position and degree of the damage, the current condition of the structure, the use function, the change trend of the structural damage and the like. The service condition of the steel frame structure can be known by carrying out damage identification on the steel frame structure, when initial small damage occurs, the damage identification and maintenance reinforcement treatment are carried out on the steel frame structure, so that the service life of the steel frame structure is prolonged, the maintenance cost is reduced, and the influence on the normal operation of the structure caused by the use of a traditional field detection method can be avoided. Therefore, the method has extremely important engineering value and practical significance for enhancing the research on the damage identification method of the steel frame structure and improving the technical level of damage identification.
In the vibration-based structural damage identification method, signal processing of structural response is one of important contents thereof. When analyzing and processing signals, the wavelet analysis can not only see the full picture of the signals, but also analyze the details of the signals, and can also keep the instantaneous characteristics of the signals and find discontinuous points and break points of data which cannot be detected by other analysis methods. When the abnormal signals are detected, the problems of signal-noise separation, characteristic parameter extraction and the like can be analyzed. Therefore, among many damage identification methods, a damage identification method based on wavelet analysis has become one of the latest hot spots.
Therefore, aiming at the steel frame structure, the mutability of response signals before and after the structural damage and the excellence of wavelet analysis processing signals are considered comprehensively, the steel frame structure damage identification method based on wavelet analysis is provided, the damage identification technical level is improved, and the performance of a steel frame structure health monitoring system is improved.
The existing patents and related technologies are searched to find that the existing structural damage identification method based on wavelet analysis mainly comprises the following steps:
(1) chenjian Gong, Zhang Yongxing, etc. a method for determining damage position of anchor rod system, CN1945307A [ p ] 2007.
A method for determining a damage position of an anchor rod system is provided. Firstly, wavelet packet decomposition is carried out on a measured signal, noise elimination is carried out by adopting a raft value, then single-branch reconstruction is carried out on a high-frequency coefficient part of the noise-eliminated signal, a reconstructed oscillogram is obtained, and finally, the damage position in the anchor rod is determined according to the mutation position of the identification signal in the oscillogram.
(2) Zones, Chung Ru, etc. A variable cross-section beam damage identification method based on node curvature and wavelet analysis, CN104750926A [ p ].2015.
A variable cross-section beam damage identification method based on node curvature and wavelet analysis is provided. Firstly, solving node curvature matrixes before and after the variable cross-section beam is damaged based on a lossless single-scale finite element model to realize damage position identification through a displacement signal of the damaged variable cross-section beam under the action of moving concentrated load, and then carrying out accurate calculation on the damage degree of the structure based on a space-time multi-scale model to obtain the damage state of the variable cross-section beam.
(3) Wu Yijiang, Chenbo, etc. the method and system for identifying the steel frame structure mutation damage, CN104458173A [ p ] 2015.
A method and a system for identifying the sudden change damage of a steel frame structure are provided. The method comprises the steps of firstly obtaining structural acceleration response, calculating a wavelet coefficient of the structure at each moment, then calculating damage identification indexes at each node of the structure by using the change rate of the wavelet coefficient, finally determining the moment when damage occurs through the change of the indexes along with time, determining the damage position through the change of the indexes at each node, and judging the damage degree through the size of the indexes at the structural loss moment.
(4)LAW S S,LI X Y,LU Z R.Structural damage detection from wavelet coefficient sensitivity with model errors[J].Journal of Engineering Mechanics,2006,132(10):1077-1087.
A structural damage identification method using wavelet coefficient sensitivity as a damage index is provided. Firstly, measuring acceleration response before and after structural damage under pulse excitation, then carrying out wavelet transformation on structural response signals of each measuring point, calculating the sensitivity of wavelet coefficients after wavelet transformation, and finally judging the damage position and the damage degree of the structure according to the peak value of the sensitivity of the wavelet coefficients of each measuring point.
(5) Application of wavelet analysis in structural damage determination and experimental studies [ J ] concrete, 2009(6): 116-.
A two-step structural damage identification method based on wavelet analysis is provided. Firstly, extracting acceleration response information before and after structural damage and carrying out wavelet transformation, then qualitatively obtaining the position of the structural damage by a hierarchical wavelet search method, and finally quantitatively obtaining structural damage degree judgment through the change condition of energy density of each frequency band before and after the damage.
(6) Dichromatic analysis and framework structure damage identification of wavelet energy curvature [ J ] Harbin university of Industrial university, 201648 (6): 170-.
A structural damage identification method using wavelet packet energy curvature difference as a damage identification index is provided. Firstly, measuring responses before and after a frame structure is damaged under the action of an earthquake, then carrying out wavelet packet transformation on the structural responses, calculating wavelet packet node energy, and finally calculating index wavelet packet energy curvature and identifying the damage position and the damage degree of the structure by using a wavelet packet energy curvature peak value.
(7) Wagner, Liulingyu, Qiaogongdong, etc. the study of two-stage damage identification and location of a space steel frame structure based on wavelet packet energy spectrum [ J ] academic newspaper of Western Ann building science and technology university (Nature science edition), 2015,47(4):492 497.
The invention provides a two-stage structural damage identification method based on a wavelet packet energy spectrum. The method comprises the steps of firstly measuring acceleration responses before and after a multi-layer multi-span frame structure is damaged under an impact load, then carrying out wavelet packet transformation on the structure acceleration responses and calculating wavelet packet energy characteristic vectors, then preliminarily judging which side of the structure the damage occurs on by calculating index energy spectrum mean deviation provided by a paper, and finally positioning which layer of the structure the damage occurs on by calculating the total energy difference change rate of displacement between index node layers provided by the paper so as to achieve the purpose of positioning the structural damage.
The existing method can be seen that the existing structural damage identification method based on wavelet analysis is only suitable for beam structures with simpler structural forms, the application in frame structures is limited to a numerical simulation stage, and the method is not applied and proved in actual engineering structures, so that damage identification research on complex multi-layer multi-span steel frame structures is insufficient.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a steel frame structure damage identification method based on wavelet packet analysis, which is applicable to a multi-layer multi-span steel frame structure, can identify the occurrence of structural damage, the position of damage, and the relative degree of damage, and can be applied to the damage identification and health monitoring of the steel frame structure. The technical scheme is as follows:
a steel frame structure damage identification method based on wavelet packet analysis comprises the following steps:
step 1: obtaining a vector set of responses of each component of the steel frame structure at positions needing to be monitored:
an accelerometer is arranged at the position of each component of the steel frame structure to be monitored, impact load is applied to the position of the steel frame structure, which is not a support, and responses measured by each measuring point are arranged to form a response vector set AuAnd Ad；
Wherein the superscript u represents the health state of the steel frame structure, i.e. the initial state; the superscript d represents the damage state of the steel frame, namely the state of the structure at a certain moment in later monitoring; the response vector set is n multiplied by m dimensional vectors, n is the structural response acquisition point number, and m is the number of the distributed points of the component;
step 2: set of response vectors AuAnd AdThe vectors of each column are processed relatively to obtain a relative response vector set BuAnd Bd：
AuMiddle element
To BuMiddle element
The operation formula of the conversion is as follows:
Admiddle element
To BdMiddle element
The operation formula of the conversion is as follows:
and step 3: set of vectors B for relative responsesuAnd BdSubjecting the vectors of each row to wavelet packet transformation to obtain a wavelet packet coefficient vector set CuAnd Cd：
Firstly, a relative response vector set B is setuAnd BdThe column vector in (1) is fitted into f (t), then wavelet transform is carried out, and wavelet packet coefficients are obtained
And
comprises the following steps:
wherein r, s, w respectively represent frequency index, scale index and position transformation parameter of wavelet packet function, psir,s,w(t) represents
Wavelet packet function, and psir,s,w(t)＝2-s/2ψr(2-st-w)，ψr(t) is calculated by the following formula:
where when r is 0, psi0(t) degenerates into a scale function phi (t), when r is 1, phi1(t) are the basis functions ψ (t), h (w) and g (w) of the wavelet packet are the integral mirror filter coefficients associated with the scale function and wavelet function;
and 4, step 4: for the wavelet packet coefficient vector set CuAnd CdCalculating the energy of the wavelet packet to obtain a wavelet packet energy characteristic vector set DuAnd Dd：
Wherein
To the direction of
The transformation formula operates as follows：
Health state wavelet component signal
Comprises the following steps:
wavelet packet energy of healthy state
Comprises the following steps:
wherein
To the direction of
The conversion formula operates as follows:
wavelet component signal of damage state
Comprises the following steps:
wavelet packet energy of damage state
Comprises the following steps:
and 5: wavelet packet energy feature vector set D is rejecteduAnd DdMiddle first column zero vector, pairThe other column vectors are operated to obtain the damage identification index EVSDR corresponding to each unitjValues, and constitutes a lesion identification row vector F:
the specific formula operation is as follows:
EVSDRj＝ak+1-ak k＝2，3，…，m-1
wherein,
and
respectively representing the mean values of wavelet packet energy characteristic vectors of a kth measuring point before and after structural damage;
and
respectively representing the standard deviation of wavelet packet energy characteristic vectors of a kth measuring point before and after structural damage; a iskRepresenting the relative difference of the wavelet packet energy characteristic vector standard deviation of the kth measuring point before and after the structural damage; EVSDRjRepresenting a damage identification index of a jth unit of the structure between a kth measuring point and a (k + 1) th measuring point of the structure;
step 6: and expressing the damage identification vector F in a curve graph form, judging whether damage occurs according to the peak value of the curve through the visualization of damage identification, determining the position where the damage occurs, and evaluating the relative degree of the damage at the same position.
The invention has the beneficial effects that: the method can be used for diagnosing the occurrence of the damage of the multi-layer and multi-span steel frame structure and monitoring the health, and can determine the occurrence position of the structural damage, the relative degree of the damage and the change of the damage degree after the damage accumulation at the same position; the microscopic characteristic of signal identification of the wavelet packet is utilized, the damage identification capability is improved, the identification index has strong robustness to noise, the damage identification capability is strong, and the method is simple.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a numerical model diagram of a 2-layer 1-span steel frame structure.
Fig. 3 is a graph showing the effect of damage recognition on a numerical model.
FIG. 4 is a diagram of IASC-ASCE benchmark structure.
FIG. 5 is a graph showing the effect of lesion recognition on the IASC-ASCE benchmark structure.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
Example 1: a2-layer 1-span space steel frame structure model is established by using finite element software ABAQUS. The horizontal and longitudinal spans of the structural model are 1000mm, the layer height is 800mm, the total height of the structure is 1600mm, and the cross section sizes of the beam and the column are 70mm multiplied by 70mm, which is shown in figure 2 in detail. Selecting the material property characteristics of the steel Q345, namely taking the density of the steel as 7.850 multiplied by 10-6The poisson ratio of kg/mm is 0.3, the elastic modulus is 2.0 multiplied by 105N/mm2Simulating damage by rigidity reduction, and presetting two damage working conditions for the structure, namely 20% damage and 30% damage respectively at No. 5 unit of the A column.
Then carrying out damage identification verification, comprising the following steps:
step one, obtaining a vector set responded at key positions of each component of the steel frame structure, and specifically realizing the following steps:
step 1.1, dividing the A column into units by 40mm, and totally 40 nodes (measuring points) except a support;
step 1.2, applying impact load on the top of the column A, wherein the peak value of the impact load is 1000N in order to ensure that the structure cannot be newly damaged and each measuring point can measure obvious response;
step 1.3, the measured responses of all measuring points are arranged and combined into a vector AuAnd AdWherein the superscript u represents the health state of the steel frame structure, i.e. the initial state; the superscript d represents the damage state of the steel frame, namely the state of the structure at a certain moment in later monitoring; and for the structural columns, the foundation support seats are sequentially arranged as starting ends, and for the structural beams, one end close to an impact point is sequentially arranged as a starting end. The response vector set is n multiplied by m dimensional vectors, n is the structural response acquisition point number, and m is the number of the distributed points of the component;
step two, calculating the anisotropic quantity set A obtained in the step oneuAnd AdWavelet packet energy eigenvector DuAnd DdThe method comprises the following concrete steps:
step 2.1 vector set AuAnd AdThe vectors of each column are processed relatively to obtain a relative response vector set BuAnd Bd；
Wherein
To the direction of
The formula for the transformation operates as follows:
wherein
To the direction of
The formula for the transformation operates as follows:
step 2.2 vector set BuAnd BdSubjecting the vectors of each row to wavelet packet transformation to obtain a wavelet packet coefficient vector set CuAnd Cd。
Firstly, a relative response vector set B is setuAnd BdThe column vector in (1) is fitted into f (t), then wavelet transform is carried out, and wavelet packet coefficients are obtained
And
comprises the following steps:
wherein r, s, w respectively represent frequency index, scale index and position transformation parameter of wavelet packet function, psir,s,w(t) denotes the wavelet packet function, andr,s,w(t)＝2-s/2ψr(2-st-w)，ψr(t) is calculated by the following formula:
where when r is 0, psi0(t) degenerates into a scale function phi (t), when r is 1, phi1(t) is the basis function of the wavelet packet ψ (t), h (w) and g (w) are the integral mirror filter coefficients associated with the scale function and wavelet function, w ∈ Z;
step 2.3 alignment of stepsStep 2.2 wavelet coefficient vector set CuAnd CdCalculating the wavelet packet energy to obtain a wavelet packet feature vector set DuAnd Dd；
Wherein
To the direction of
The conversion formula operates as follows:
health state wavelet component signal
Comprises the following steps:
wavelet packet energy of healthy state
Comprises the following steps:
wherein
To the direction of
The conversion formula operates as follows:
wavelet component signal of damage state
Comprises the following steps:
state of injuryEnergy of wavelet packet
Comprises the following steps:
step three, according to the wavelet packet energy feature vector set D obtained in the step twouAnd DdCalculating a damage identification vector F, and identifying the damage of the steel frame structure, wherein the specific implementation steps are as follows:
step 3.1 reject vector set DuAnd DdComputing the zero vectors of the first row to obtain the damage identification index EVSDR corresponding to each unitjValues and constitutes a lesion identification row vector F. To be provided with
And
to ENSDRjThe conversion is an example, and the specific formula operation is as follows:
EVSDRj＝ak+1-ak k＝2，3，…，m-1
wherein,
and
respectively representing the mean values of wavelet packet energy characteristic vectors of a kth measuring point before and after structural damage;
and
respectively representing the standard deviation of wavelet packet energy characteristic vectors of a kth measuring point before and after structural damage; a iskRepresenting the relative difference of the wavelet packet energy characteristic vector standard deviation of the kth measuring point before and after the structural damage; EVSDRjAnd representing the damage identification index of the jth unit of the structure between the kth measuring point and the (k + 1) th measuring point of the structure.
And 3.2, representing the damage identification vector F in a curve graph mode, so that the visualization of damage identification can be achieved, as shown in fig. 3. And judging the 5 th unit of structural damage according to the peak value of the curve appearing at the 5 th unit number, and evaluating that the damage of 30 percent preset at the 5 th unit is stronger than the damage of 20 percent preset at the 5 th unit through peak value comparison.
Example 2: the American health monitoring task force proposed a benchmark structure and the benchmark structure was tested for damage at the university of Columbia, the British genus, Canada. The benchmark structure is a 4-layer 2 x 2 span steel frame structure model, the plane size is 2.5m x 2.5m, the layer height is 0.9m, and the total height is 3.6m, as shown in fig. 4. The damage is simulated by removing the diagonal brace, and under the impact test, the working condition 2 (all the floor east-side supports are removed) is taken as the original state, the working condition 6 (all the floor east-side supports are removed, the second floor north-side supports are removed) is taken as the damaged state, namely the second floor is damaged.
Then carrying out damage identification verification, comprising the following steps:
step one, obtaining a vector set responded at key positions of each component of the steel frame structure, and specifically realizing the following steps:
step 1.1, one FBA accelerometer is placed at each floor, including a support, and 5 FBA accelerometers are measured at 5 measuring points in total;
step 1.2, applying hammering excitation to a layer of southeast corner of the steel frame structure;
step 1.3, the measured responses of all measuring points are arranged and combined into a vector AuAnd AdWherein the superscript u represents the health state of the steel frame structure, i.e. the initial state; the superscript d represents the damage state of the steel frame, namely the state of the structure at a certain moment in later monitoring; and for the structural columns, the foundation support seats are sequentially arranged as starting ends, and for the structural beams, one end close to an impact point is sequentially arranged as a starting end. The response vector set is n multiplied by m dimensional vectors, n is the structural response collection point number, and m is the number of the distributed points of the component.
Step two, calculating the anisotropic quantity set A obtained in the step oneuAnd AdWavelet packet energy eigenvector DuAnd DdThe method comprises the following concrete steps:
step 2.1 vector set AuAnd AdThe vectors of each column are processed relatively to obtain a relative response vector set BuAnd Bd(ii) a Wherein
To the direction of
The formula for the transformation operates as follows:
wherein
To the direction of
The formula for the transformation operates as follows:
step 2.2 vector set BuAnd BdWavelet processing of each column vectorPerforming packet transformation to obtain wavelet packet coefficient vector set CuAnd Cd(ii) a Firstly, a relative response vector set B is firstly obtaineduAnd BdThe column vector in (1) is fitted into f (t), then wavelet transform is carried out, and wavelet packet coefficients are obtained
And
comprises the following steps:
wherein r, s, w respectively represent frequency index, scale index and position transformation parameter of wavelet packet function, psir,s,w(t) denotes the wavelet packet function, andr,s,w(t)＝2-s/2ψr(2-st-w)，ψr(t) is calculated by the following formula:
where when r is 0, psi0(t) degenerates into a scale function phi (t), when r is 1, phi1(t) is the basis function of the wavelet packet ψ (t), h (w) and g (w) are the integral mirror filter coefficients associated with the scale function and wavelet function, w ∈ Z;
step 2.3 vector set C of wavelet coefficients in step 2.2uAnd CdCalculating the wavelet packet energy to obtain a wavelet packet feature vector set DuAnd Dd；
Wherein
To the direction of
The conversion formula operates as follows:
health state wavelet component signal
Comprises the following steps:
wavelet packet energy of healthy state
Comprises the following steps:
wherein
To the direction of
The conversion formula operates as follows:
wavelet component signal of damage state
Comprises the following steps:
wavelet packet energy of damage state
Comprises the following steps:
step three, according to the wavelet packet energy feature vector set D obtained in the step twouAnd DdCalculating a damage identification vector F, and identifying the damage of the steel frame structure, wherein the specific implementation steps are as follows:
step 3.1 reject vector set DuAnd DdComputing the zero vectors of the first row to obtain the damage identification index EVSDR corresponding to each unitjValues and constitutes a lesion identification row vector F. To be provided with
And
to ENSDRjThe conversion is an example, and the specific formula operation is as follows:
EVSDRj＝ak+1-ak k＝2，3，…，m-1
wherein EVSDRjAnd representing the damage identification index of the structural unit j between the kth measuring point and the (k + 1) th measuring point of the structure.
And 3.2, representing the damage identification vector F in a curve graph mode, so that the visualization of damage identification can be achieved, as shown in fig. 5. Judging that the structure is damaged according to the peak value of the curve appearing in the number of the layer 2, and determining the layer 2 with the damaged structure.
Claims (1)
1. A steel frame structure damage identification method based on wavelet packet analysis is characterized by comprising the following steps:
step 1: obtaining a vector set of responses of each component of the steel frame structure at positions needing to be monitored:
an accelerometer is arranged at the position of each component of the steel frame structure to be monitored, impact load is applied to the position of the steel frame structure, which is not a support, and responses measured by each measuring point are arranged to form a response vector set AuAnd Ad；
Wherein the superscript u represents the health state of the steel frame structure, i.e. the initial state; the superscript d represents the damage state of the steel frame, namely the state of the structure at a certain moment in later monitoring; for the structural columns, the foundation support is taken as an initial end to be sequentially arranged, and for the structural beams, one end close to an impact point is taken as an initial end to be sequentially arranged; the response vector set is n multiplied by m dimensional vectors, n is the structural response acquisition point number, and m is the number of the distributed points of the component;
step 2: set of response vectors AuAnd AdThe vectors of each column are processed relatively to obtain a relative response vector set BuAnd Bd：
AuMiddle element
To BuMiddle element
The operation formula of the conversion is as follows:
Admiddle element
To BdMiddle element
The operation formula of the conversion is as follows:
and step 3: set of vectors B for relative responsesuAnd BdSubjecting the vectors of each row to wavelet packet transformation to obtain a wavelet packet coefficient vector set CuAnd Cd：
Firstly, a relative response vector set B is setuAnd BdThe column vector in (1) is fitted into f (t), then wavelet transform is carried out, and wavelet packet coefficients are obtained
And
comprises the following steps:
wherein r, s, w respectively represent frequency index, scale index and position transformation parameter of wavelet packet function, psir,s,w(t) denotes the wavelet packet function, andr,s,w(t)＝2-s/2ψr(2-st-w)，ψr(t) is calculated by the following formula:
where when r is 0, psi0(t) degenerates into a scale function phi (t), when r is 1, phi1(t) are the basis functions ψ (t), h (w) and g (w) of the wavelet packet are the integral mirror filter coefficients associated with the scale function and wavelet function;
and 4, step 4: for the wavelet packet coefficient vector set CuAnd CdCalculating the energy of the wavelet packet to obtain a wavelet packet energy characteristic vector set DuAnd Dd：
Wherein
To the direction of
The conversion formula operates as follows:
health state wavelet component signal
Comprises the following steps:
wavelet packet energy of healthy state
Comprises the following steps:
wherein
To the direction of
Conversion formulaThe operation is as follows:
wavelet component signal of damage state
Comprises the following steps:
wavelet packet energy of damage state
Comprises the following steps:
and 5: wavelet packet energy feature vector set D is rejecteduAnd DdComputing the zero vectors of the first row to obtain the damage identification index EVSDR corresponding to each unitjValues, and constitutes a lesion identification row vector F:
the specific formula operation is as follows:
EVSDRj＝ak+1-ak，k＝2，3，…，m-1
wherein,
and
respectively representing the mean values of wavelet packet energy characteristic vectors of a kth measuring point before and after structural damage;
and
respectively representing the standard deviation of wavelet packet energy characteristic vectors of a kth measuring point before and after structural damage; a iskRepresenting the relative difference of the wavelet packet energy characteristic vector standard deviation of the kth measuring point before and after the structural damage; EVSDRjRepresenting a damage identification index of a jth unit of the structure between a kth measuring point and a (k + 1) th measuring point of the structure;
step 6: and expressing the damage identification vector F in a curve graph form, judging whether damage occurs according to the peak value of the curve through the visualization of damage identification, determining the position where the damage occurs, and evaluating the relative degree of the damage at the same position.
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