A structural damage identification method based on overlapping group sparse model

Abstract

The application discloses a structural damage identification method based on an overlapping group sparse model, and comprises the following steps: arranging a sensor to collect structural excitation and response information; establishing a finite element model of a healthy structure; taking a unit stiffness change coefficient as a design variable; establishing a sensitivity matrix according to the sensitivity of a modal parameter to the change amount of the design variable; performing modal analysis on a damaged structure; obtaining the change amount of the modal parameter of the damaged structure and the finite element model; setting the number of overlaps and the number of non-overlaps of a sparse group according to the number of units of the structure; constructing a corresponding grouping matrix and rearranging the sensitivity matrix; solving a target function by using a split Bregman algorithm; considering the damage characteristic constraint design variable; iterating until convergence; and positioning and quantifying the damage according to the identification result. The method provided by the application is suitable for the case that the structural unit is divided into more units, can realize accurate positioning and quantification of the damage, and has high engineering application value.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of structural health monitoring, in particular to a structural damage identification technology, and in particular to a structural damage identification method based on overlapping group sparse model. BACKGROUND

[0002] With the gradual enhancement of China's economic strength, more and more civil engineering structures are put into application. During the service period of civil engineering structures, in addition to the long-term effects of material performance degradation and external working load, they are inevitably affected by various natural factors, so that civil engineering structures inevitably accumulate damage during long-term service. The accumulation of damage will cause the bearing capacity of civil engineering structures to continuously decrease, eventually leading to structural failure and collapse, causing loss of life and property. Therefore, in order to ensure the healthy service of civil engineering structures, it is necessary to detect the potential damage of the structure to provide a reference for the maintenance and repair of the structure. In recent years, there have been many research results on structural damage identification methods.

[0003] The patent document CN114510762A discloses a "structural damage identification method and system based on time series model coefficient sensitivity", which first establishes a multi-dimensional ARMAX model corresponding to the structural motion equation, then constructs the sensitivity matrix of the autoregressive coefficients of the model and the structural stiffness reduction coefficient, and finally solves the problem using sparse regularization algorithm and realizes damage positioning and quantification according to the value and position of the non-zero elements in the identification result. This method simplifies each floor of the structure to a concentrated mass for damage identification, although the identification accuracy is high, but due to the too few elements divided for the structure, the damage degree is easily underestimated, and it is difficult to accurately locate the damage.

[0004] The patent document CN110487519A discloses a "structural damage identification method based on ALO-INM and weighted trace norm", which first introduces the frequency relative change rate and modal confidence criterion into the structural damage identification constrained optimization problem, then constructs the objective function of the damage identification problem based on the weighted strategy and trace sparse regularization, and finally iteratively solves the objective function of the problem using ALO-INM algorithm. This method introduces trace sparse regularization to improve the ill-posedness of the problem, and effectively identifies structural damage using only the first five modal parameters, but under the influence of noise, the identification result has many misjudgments, which is not conducive to checking the actual damage position in actual application. In addition, the ALO-INM algorithm is a non-deterministic algorithm, and the identification result has randomness, and the damage degree of the structure cannot be determined by one calculation. SUMMARY

[0005] The purpose of the present application is to solve the above-mentioned defects in the prior art, provide a structure damage identification method based on overlapping group sparse model, which can effectively identify the damage of continuous units, and has simple calculation and high identification precision. When a finite element model is used to identify the damage of an actual civil engineering structure, in order to improve the positioning accuracy, the structure needs to be divided into as many units as possible, at this time, the damage may cause the stiffness of multiple continuous units of the structure to change, the characteristics of the damage at this time are considered to be introduced into the structure damage identification problem, and the problem is constrained by combining the overlapping group sparse model, so that the ill-posedness of the problem can be effectively improved, and the structure damage can be effectively positioned and quantified.

[0006] The purpose of the present application can be achieved by adopting the following technical solutions:

[0007] A structure damage identification method based on an overlapping group sparse model, the structure damage identification method comprising the following steps:

[0008] S1, arranging force sensors on the excitation points of the structure and arranging acceleration sensors on the structure;

[0009] S2, establishing a finite element model of a healthy structure according to the structure parameters, taking the unit stiffness change coefficient of the finite element model as a design variable, and establishing a sensitivity matrix according to the sensitivity of the change amount of the design variable to the modal parameters of the finite element model;

[0010] S3, collecting excitation information and response information of the damaged structure for modal analysis, and obtaining the change amount of the modal parameters of the damaged structure and the finite element model;

[0011] S4, setting the number of overlapping groups and the number of non-overlapping groups of the sparse groups for the change amount of the design variable according to the number of units of the structure, constructing a corresponding grouping matrix and rearranging the sensitivity matrix, and establishing an objective function of the structure damage identification problem based on the overlapping group sparse model;

[0012] S5, solving the objective function by using a split Bregman algorithm;

[0013] S6, considering the damage characteristics, and constraining the design variable;

[0014] S7, iteratively updating the finite element model until convergence, and positioning and quantifying the structure damage according to the identification result.

[0015] Further, in the step S1, the excitation points are selected and the force sensors are arranged away from the modal nodes of each order and the positions with large structure displacement, and the acceleration sensors are arranged on the unit nodes of the structure, wherein the measurement direction of the sensor is consistent with the excitation direction.

[0016] Further, in the step S2, the finite element model of the healthy structure is established according to the structure parameters as follows:

[0017] To effectively locate and quantify the structural damage, it is necessary to establish the approximate relationship between modal parameters and physical parameters by sensitivity analysis method, assuming that the structure damage only causes the change of the structural unit stiffness, taking the element stiffness change coefficient of the finite element model as the design variable, the sensitivity of the i-th order natural frequency f i of the structure with respect to the design variable α j of the j-th element stiffness is the i-th order mode shape of the structure the sensitivity of the i-th order mode shape of the structure with respect to the design variable α j of the j-th element stiffness is wherein, K and M are the overall stiffness matrix and the overall mass matrix of the structure respectively, K j is the element stiffness matrix of the j-th element of the structure, n is the number of elements of the structure, is the s-th order mode shape of the structure, the sensitivity matrix is established by combining the sensitivity of the natural frequency and the mode shape:

[0018]

[0019] wherein, i = 1, 2, …, m, m is the order of the modal parameter, S f and are the sensitivity matrix of the natural frequency and the mode shape respectively.

[0020] Further, the excitation information and the response information of the damaged structure are collected in the step S3 for modal analysis, and the modal parameters of each order of the damaged structure are obtained, which are compared with the modal parameters of the finite element model. Since multiple indexes are used for damage identification, the identification accuracy of the problem can be effectively improved, and therefore the damage index of the problem is set according to the change amount of the natural frequency and the change amount of the mode shape of the damaged structure and the finite element model, so as to obtain the change amount Δf of the modal parameters of the damaged structure and the finite element model:

[0021]

[0022] wherein, Δf f and are the difference of the natural frequency and the mode shape of the structure respectively.

[0023] Further, in the step S4, according to the number of elements of the structure, the change amount Δα = {Δα1, Δα2, …, Δα n} T of the design variable is set to the overlap number N r and the non-overlap number N nrwherein the setting of the overlap number and the non-overlap number is also related to the damage characteristics of the structure, when the structure is divided into more units, local damage can cause the stiffness of continuous multiple units to change, at this time the overlap number should be increased and the non-overlap number should be reduced, the change amount of the design variable is divided into g sparse groups according to the overlap number and the non-overlap number of the sparse group, wherein is a positive integer, the sparse groups are sorted to obtain the change amount of the overlap design variable The relationship between the change amount of the design variable and the change amount of the overlap design variable is:

[0024]

[0025] Ψ is a grouping matrix constructed according to the relationship between the change amount of the design variable and the change amount of the overlap design variable;

[0026] The overlap sensitivity matrix S is constructed based on the grouping matrix and the rearrangement of the sensitivity matrix r so that the column number of the overlap sensitivity matrix and the row number of the change amount of the overlap design variable match at this time, the overlap sensitivity matrix can be constructed according to the sensitivity matrix and the grouping matrix:

[0027] S r = SΨ

[0028] In order to solve the change amount of the design variable, considering that the structure damage identification problem at this time is an optimization problem, therefore, according to the approximate relationship between the modal parameter change amount of the damaged structure and the finite element model, the overlap sensitivity matrix and the change amount of the overlap design variable, the objective function of the structure damage identification problem based on the overlap group sparse model is established:

[0029]

[0030] wherein ||·||2 represents the 2-norm, represents the square of the 2-norm, λ>0 is the regularization parameter of the overlap group sparse model, p is the number of the sparse group, p=1,2,…,g, p represents the coefficient of the pth group, and Γ is the sparse conversion matrix.

[0031] Further, in the step S5, the split Bregman algorithm proposed in the document "J.Zou and Y.Fu, Split Bregman algorithms for sparse group lasso with application to MRI reconstruction, Multidimensional Syst.Signal Process." is used to solve the objective function of the structural damage identification problem, the algorithm is a deterministic algorithm, and the unique optimal solution of the problem can be obtained, and the calculation is effectively simplified, and the change amount of the overlapping design variable obtained by the algorithm solving is used to convert the change amount of the overlapping design variable into the change amount of the design variable based on the grouping matrix.

[0032] Further, in the step S6, due to the influence of the ill-posedness of the structural damage identification problem and the measurement noise and other factors, the identification result often appears the phenomenon of local stiffness strengthening, in order to improve the unreasonable problem of the identification result, the value of the design variable needs to be limited in a reasonable range, so that the identification accuracy and efficiency are effectively improved, considering the damage characteristics, the unit stiffness will not appear the phenomenon of negative stiffness and stiffness strengthening, and the following constraint is added to the obtained design variable:

[0033] 0≤α j ≤1.

[0034] Further, in the step S7, considering that the sensitivity of the modal parameter is only an approximate relationship between the change amount of the design variable and the change amount of the modal parameter, the design variable of the finite element model needs to be iteratively updated until convergence, and the change amount of the design variable obtained by solving each iteration is added, so that the damage can be positioned and quantified according to the final change amount of the design variable, wherein the position of the non-zero element represents the unit position of the damage, and the value of the non-zero element corresponds to the damage degree of the damage unit.

[0035] The present application has the following advantages and effects relative to the prior art:

[0036] 1. The present application divides the structure into units by using the finite element analysis method, calculates the sensitivity of the natural frequency and the mode shape to the design variable of the unit stiffness, deduces the relationship between the change of the structural unit stiffness and the change amount of the modal parameter, establishes the sensitivity matrix, and realizes quantization of the damage through the change of each unit stiffness.

[0037] 2. The overlapping group sparse model is combined, the change amount of the design variable is grouped and the regularization method is used to constrain the solution space, the objective function of the structural damage identification problem is established, and the split Bregman algorithm is used to solve it, which can effectively reduce the damage misjudgment, improve the identification accuracy and obtain the unique solution of the problem.

[0038] 3、According to the damage characteristics, the design variables of the identification result are constrained, the rationality of the identification result can be effectively improved, and it is more suitable for practical civil engineering structures.

[0039] 4、The application is suitable for the case that the structural unit is divided more, and can realize accurate positioning and quantification of structural damage, has strong innovation and great application prospect. The application can realize real-time damage monitoring of civil engineering structures, provides the possibility for effectively identifying the position and degree of structural damage, and achieves the purpose of ensuring the service safety of civil engineering structures. BRIEF DESCRIPTION OF DRAWINGS

[0040] The drawings described herein are used to provide further understanding of the application, constitute a part of the application, the illustrative embodiments of the application and the description thereof are used to explain the application, and do not constitute improper limitation on the application. In the drawings:

[0041] Figure 1 is a flowchart of a structural damage identification method based on the overlapping group sparse model disclosed by the application;

[0042] Figure 2 is a structural model diagram represented in embodiment 1 of the application;

[0043] Figure 3 is a damage identification result diagram of the simply supported beam model damage condition in embodiment 1 of the application;

[0044] Figure 4 is a structural model diagram represented in embodiment 2 of the application;

[0045] Figure 5 is a damage identification result diagram of the truss model damage condition in embodiment 2 of the application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical scheme and advantages of the embodiments of the application more clear, the technical scheme in the embodiments of the application will be clearly and completely described below in combination with the drawings in the embodiments of the application. Obviously, the described embodiments are a part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0047] Embodiment 1

[0048] The main implementation process of the structural damage identification of the application is as shown in Figure 1 The specific steps of the structural damage identification method based on the overlapping group sparse model are as follows:

[0049] S1, arranging force sensors on the excitation points of the structure and arranging acceleration sensors on the structure;

[0050] S2, establishing a finite element model of the healthy structure according to the structural parameters, taking the unit stiffness change coefficient of the finite element model as a design variable, and establishing a sensitivity matrix according to the sensitivity of the change amount of the design variable to the modal parameters of the finite element model;

[0051] S3, collecting excitation information and response information of the damaged structure for modal analysis, and obtaining the change amount of the modal parameters of the damaged structure and the finite element model;

[0052] S4, setting the number of overlapping groups and the number of non-overlapping groups of the design variable change amount according to the number of units of the structure, constructing a corresponding grouping matrix and rearranging the sensitivity matrix, and establishing an objective function of the structure damage identification problem based on the overlapping group sparse model;

[0053] S5, solving the objective function by using the split Bregman algorithm;

[0054] S6, considering the damage characteristics and constraining the design variable;

[0055] S7, iteratively updating the finite element model until convergence, and positioning and quantifying the structural damage according to the identification result.

[0056] Taking a simply supported beam model as the research object, the implementation process of the numerical simulation structure damage identification technology is described.

[0057] The numerical model diagram is shown in Figure 2 The total length of the simply supported beam model is 32m, the cross-sectional area is 4.299m 2 , the elastic modulus and density of the structural material are 46.805GPa and 2645.066kg / m 3 , Rayleigh damping is used, the first two damping ratios are ξ1=ξ2=0.02, and the noise level is 5%. The damage conditions are: the damage degree of unit 11 is 3%, the damage degree of unit 12 is 7%, the damage degree of unit 13 is 12%, the damage degree of unit 14 is 6%, and the damage degree of unit 15 is 2%. The specific implementation steps of the structure damage identification are as follows:

[0058] (1) According to the structural design parameters, a finite element model of the structure is established by using beam elements, and the simply supported beam model is discretized into 40 units. The first 4 order modal parameters are used for structure damage identification, so the nodes and positions with large displacement of the first 4 order modal shapes are avoided, and the excitation position and direction of the load are selected as the y direction of the 19th node of the structure. Acceleration measuring points are arranged on nodes 2-40 to measure the y direction acceleration response of each node.

[0059] (2) Take the unit stiffness change coefficient of the finite element model as the design variable α j , the sensitivity of the structural natural frequency and the mode shape Establish the sensitivity matrix S.

[0060] (3) Modal analysis is performed on the damaged structure to obtain the natural frequency and mode shape of the damaged structure. The natural frequency and mode shape of the finite element model are compared, and the modal parameter change amount Δf of the damaged structure and the finite element model is obtained according to the difference between the two.

[0061] (4) Considering that the structure is discretized into 40 units, the damage will cause the stiffness of multiple consecutive units to change, and the overlap number N r = 2 and the non-overlap number N nr = 4 are set. According to the overlap number and the non-overlap number, the change amount Δα of the design variable is divided into 10 sparse groups. The change amount of the overlap design variable can be obtained by sorting the sparse groups The grouping matrix Ψ at this time can be obtained from the formula The overlap sensitivity matrix S r is constructed by rearranging the sensitivity matrix S based on the grouping matrix. According to the modal parameter change amount Δf of the damaged structure and the finite element model and the overlap sensitivity matrix S r , the objective function of the structure damage identification problem based on the overlap group sparse model is established

[0062] (5) The split Bregman algorithm is used to solve the objective function, where the weight of the algorithm is set to 1. The solution obtained at this time is the change amount of the overlap design variable, which needs to be converted to the change amount of the design variable by the formula

[0063] (6) Considering the damage characteristics, constraints 0≤α j ≤1 are added to the obtained design variable.

[0064] (7) The stiffness of the model is iteratively updated until convergence. The location of the damaged unit is determined according to the position of the non-zero element in the identification result, and the damage degree of the damaged unit corresponds to the size of the non-zero element.

[0065] The structure damage identification result is shown in Figure 3 From Figure 3 It can be seen that a structure damage identification method based on an overlap group sparse model can accurately locate the damage position and quantify the damage degree of the damage condition of the continuous unit stiffness reduction in this specific embodiment, and has less misjudgment, higher damage identification accuracy and stronger robustness.

[0066] ​From the above examples, the present application can achieve accurate positioning of structural damage by the specific steps implemented, with less damage misjudgment units under the influence of noise, and the damage unit position can be identified.

[0067] Example 2

[0068] A truss model is taken as the research object to describe the implementation process of the numerical simulation structural damage identification technology.

[0069] The numerical model diagram is shown in Figure 4 Each rod has a cross-sectional area of 2.5x10 -3 m 2 , the elastic modulus and density of the rod material are 70GPa and 2770kg / m 3 , respectively, the length of each rod in the horizontal and vertical directions is 1.52m, Rayleigh damping is used, and the first two damping ratios are ξ1=ξ2=0.01, and the noise level is 5%. The damage condition is that the damage degree of 3 units is 15%. The specific implementation steps of structural damage identification are as follows:

[0070] (1) According to the structural design parameters, a finite element model of the structure is established using a rod element, and the entire model has 31 units. The first 3 modal parameters are used for structural damage identification, the excitation position and direction of the load are the y direction of the 12th node of the structure, and acceleration measuring points are arranged on all nodes except the 1st and 7th nodes.

[0071] (2) Refer to steps (2) and (3) in Example 1 to obtain the sensitivity matrix S and the modal parameter variation Δf.

[0072] (3) Considering that the structure has 31 units at this time, the overlap number N r =1 and the non-overlap number N nr =3 of the sparse group are set, and the change Δα of the design variable is divided into 10 sparse groups at this time. Refer to steps (4) in Example 1 to establish the objective function of the structural damage identification problem based on the sparse model of the overlap group.

[0073] (4) Refer to steps (5)-(7) in Example 1 to solve the objective function and constrain the design variable, and after iterative convergence, the damage is located and quantified according to the identification result.

[0074] The structural damage identification result is shown in Figure 5 From Figure 5 it can be seen that the structural damage identification method based on the sparse model of the overlap group can accurately identify the damage condition of a single unit with stiffness reduction in this specific example, has high identification accuracy, and the misjudgment damage degree is very small, which does not affect the judgment of the true damage position.

[0075] The comparison of the identification results of the two embodiments shows that the structural damage identification method based on the overlapping group sparse model can identify different structures and different damage conditions, and has high identification accuracy by dividing the change of the design variable into multiple sparse groups and solving the sparse groups.

[0076] The above embodiments are preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application should be equivalent replacement methods, and are included in the protection scope of the present application.

Claims

1. A structural damage identification method based on overlapping group sparse model, characterized in that: The structural damage identification method comprises the following steps: S1. Arrange force sensors at the excitation points of the structure and arrange acceleration sensors on the structure; S2. Establish a finite element model of the healthy structure based on the structural parameters, use the unit stiffness change coefficient of the finite element model as the design variable, and establish a sensitivity matrix based on the sensitivity of the modal parameters of the finite element model to the change of the design variable; S3, collecting excitation information and response information of the damaged structure to perform modal analysis and obtain the modal parameter changes of the damaged structure and the finite element model; S4, according to the number of units of the structure, set the overlapping number and non-overlapping number of sparse groups for the change of the design variable, construct the corresponding grouping matrix and rearrange the sensitivity matrix, and establish the objective function of the structural damage identification problem based on the overlapping group sparse model; in the step S4, according to the number of units of the structure, the change of the design variable Δα={Δα1,Δα2,…,Δα n } T Set the overlap number N of the sparse groups r and the number of non-overlapping N nr , divide the change of the design variable into g sparse groups according to the overlapping and non-overlapping numbers of the sparse groups, where Sort the sparse groups to obtain the changes in overlapping design variables The relationship between the change in the design variable and the change in the overlapping design variable is: Where Ψ is the grouping matrix constructed based on the relationship between the change of the design variables and the change of the overlapping design variables; Based on the grouping matrix, the sensitivity matrix is ​​rearranged and the overlapping sensitivity matrix is ​​constructed as: S r =SΨ, According to the modal parameter changes and overlapping sensitivity matrix of the damaged structure and the finite element model, the objective function of the structural damage identification problem based on the overlapping group sparse model is established: Where ||·||2 represents the 2-norm, represents the square of the 2-norm, λ>0 is the regularization parameter of the overlapping group sparse model, and p is the number of the sparse group, p=1,2,…,g,(·) p represents the coefficient of the pth group, Γ is the sparse transformation matrix; S5, using the split Bregman algorithm to solve the objective function; S6. Consider damage characteristics and constrain design variables; S7. Iteratively update the finite element model until convergence, and locate and quantify the structural damage based on the identification results.

2. The structural damage identification method based on overlapping group sparse model according to claim 1 is characterized in that: In step S2, the finite element model of the healthy structure is established according to the structural parameters as follows: Assuming that the structural damage only causes the change of the structural unit stiffness, the unit stiffness change coefficient of the finite element model is used as the design variable, and the i-th order natural frequency of the structure f i Design variable α about the stiffness of the jth element j The sensitivity is The i-th vibration mode of the structure Design variable α about the stiffness of the jth element j The sensitivity is Among them, K and M are the overall stiffness matrix and overall mass matrix of the structure respectively, K j is the element stiffness matrix of the jth element of the structure, n is the number of elements in the structure, For the s-order vibration mode of the structure, the sensitivity matrix is ​​established by combining the natural frequency and vibration mode sensitivity: Where i = 1, 2, ..., m, m is the order of the modal parameter, S f and are the sensitivity matrices of natural frequencies and mode shapes, respectively.

3. The structural damage identification method based on overlapping group sparse model according to claim 1 is characterized in that: In step S3, the excitation information and response information of the damaged structure are collected for modal analysis to obtain the modal parameters of each order of the damaged structure. The modal parameters of the finite element model are compared to obtain the modal parameter change Δf between the damaged structure and the finite element model: Where Δf f and are the natural frequency and mode shape difference of the structure, respectively.

4. The structural damage identification method based on overlapping group sparse model according to claim 1 is characterized in that: In step S5, the split Bregman algorithm is used to solve the objective function of the structural damage identification problem, obtain the changes of overlapping design variables, and convert the changes of overlapping design variables into changes of design variables based on the grouping matrix.

5. The structural damage identification method based on overlapping group sparse model according to claim 2 is characterized in that: In step S6, due to the ill-posedness of the structural damage identification problem and the influence of measurement noise, the identification results often show the phenomenon of local stiffness enhancement. In order to improve the unreasonable identification results, the following constraints are added to the obtained design variables considering the damage characteristics: 0≤α j ≤1。 6. The structural damage identification method based on overlapping group sparse model according to claim 1 is characterized in that: In step S7, the design variables of the finite element model are iteratively updated until convergence, and the position of the damaged unit is determined according to the position of the non-zero elements in the identification result. The value of the non-zero element corresponds to the damage degree of the damaged unit.

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