CN106897543B - Beam structure damage identification method of modal compliance curvature matrix norm - Google Patents

Beam structure damage identification method of modal compliance curvature matrix norm Download PDF

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CN106897543B
CN106897543B CN201710274079.0A CN201710274079A CN106897543B CN 106897543 B CN106897543 B CN 106897543B CN 201710274079 A CN201710274079 A CN 201710274079A CN 106897543 B CN106897543 B CN 106897543B
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CN106897543A (en
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唐盛华
苏彬建
张学兵
罗正东
李永亮
秦付倩
周楠
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Xiangtan University
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Abstract

The invention discloses a beam structure damage identification method of modal compliance curvature matrix norm. The invention comprises the following steps: obtaining modal flexibility matrixes before and after the beam structure is damaged through modal testing; curvature of a compliance matrix before and after the beam structure is damaged is solved, then norms are sequentially solved for each column vector of the compliance curvature matrix, and the structure damage is positioned by using the norm difference; and calculating the damage degree of the beam structure node according to the relative change of the norm of the compliance curvature matrix before and after damage, and further calculating to obtain the unit damage degree. The method can effectively position the damage of the beam structure under single-damage and multi-damage working conditions, can accurately identify the damage degree, well overcomes the defect that the existing modal flexibility curvature index cannot identify the damage degree, and can be applied to nondestructive detection and damage degree evaluation of the beam structure.

Description

Beam structure damage identification method of modal compliance curvature matrix norm
Technical Field
The invention belongs to the technical field of structural health monitoring, and particularly relates to a beam structure damage identification method of modal compliance curvature matrix norm in a beam structure nondestructive testing technology.
Background
The bridge structure is largely applied to the civil engineering field with important effect on national economic development, such as highways, high-speed railways and the like, and is traffic throat and national economic development lifeline engineering. The health condition of the urban public health monitoring system is gradually concerned by people, and at present, health monitoring systems are installed on newly-built important bridge structures in many countries, such as hong Kong Qingma bridge, Sutong bridge, Yangtze river highway bridge, Japan Ming Shi strait bridge and the like. How to analyze a large amount of collected data and judge the state of the structure is a research hotspot at home and abroad.
Structural damage identification is an important component of bridge structure health monitoring systems, and damage detection generally includes at least three aspects: (1) judging whether the structure is damaged or not; (2) possible damage locations of the structure; (3) degree of damage to the structure. Since the damage causes the reduction of the structural rigidity and further causes the change of structural modal parameters, the structural damage can be identified by the modal parameters, such as a frequency method, a mode curvature method, a flexibility curvature method and the like. Whether a structure is damaged or not can be judged by frequency change, but damage positioning cannot be effectively carried out because the frequency is an overall parameter of the structure. The vibration mode is related to the position information of the structure, so that damage positioning can be carried out, but the problems that the damage at a node of a curvature mode is not sensitive and the damage degree cannot be effectively reflected exist, and because the vibration mode curvature method does not use frequency information, the effect of the vibration mode curvature method is generally not good when the damage identification method comprehensively utilizing the vibration mode and the frequency is used, such as an improved curvature mode method, a flexibility curvature method and the like.
The structure flexibility matrix can be accurately established by a low-order mode, and the sensitivity to damage is higher than the frequency and the mode shape, so the structure flexibility matrix becomes an important method in structure damage identification. The early flexibility damage index adopts modal flexibility difference to position damage in a mode of a maximum value, the effect is not ideal, and then research is mainly focused on flexibility curvature damage indexes, such as the index of uniform load surface curvature difference; establishing a flexibility matrix curvature index by using the maximum value of the array vector of the flexibility curvature matrix and the main diagonal elements; and performing twice difference on the rows and the columns of the flexibility matrix difference, and using the absolute maximum value of the columns or diagonal elements as a structural damage detection index.
Although much research work is carried out on the flexibility indexes, the flexibility indexes mainly focus on the aspect of damage positioning, and the existing indexes cannot effectively identify the damage degree.
Disclosure of Invention
The invention aims to provide a beam structure damage identification method of modal flexibility curvature matrix norm, which can effectively perform damage positioning of single damage and multiple damage working conditions on a beam structure and accurately identify the damage degree, aiming at the problems that the damage positioning of the existing modal flexibility curvature damage index is insufficient and the damage degree cannot be identified.
The purpose of the invention is realized by the following technical scheme: the method for identifying the beam structure damage of the modal compliance curvature matrix norm comprises the following steps:
(1) modal parameters before and after the beam structure is damaged are respectively obtained through testing, and a flexibility matrix is respectively calculated according to the frequency and the vibration mode;
(2) curvature of a compliance matrix before and after the beam structure is damaged is solved, then norms are sequentially solved for each column vector of the compliance curvature matrix, and the structure damage is positioned by using the norm difference;
(3) and calculating the damage degree of the beam structure node according to the relative change of the norm of the compliance curvature matrix before and after damage, and further calculating to obtain the unit damage degree.
Specifically, in the step (1), the number of the measuring points of each span is not less than 8 in the modal parameter test before and after the beam structure is damaged, and the positions of the measuring points before and after the damage are arranged identically.
Specifically, in the step (1), the modal order obtained by the test is not less than 3.
Specifically, in the step (1), the mode parameter test adopts a measurable excitation method to directly measure the mode shape normalized with respect to the mass matrix, or adopts a method of only measuring output and establishes the mass matrix through a finite element model of the beam structure, and after normalizing the mode shape to the mass matrix, a mode compliance matrix F expressed by frequency and mode shape can be obtained:
Figure BDA0001278171260000031
wherein phi is [ phi ]1,φ2,L,φm]Is a mode matrix, m is a mode order, phii＝[φi1φi2L φin]TIs the ith order mode vector, n is the number of measuring points,
Figure BDA0001278171260000032
as a diagonal matrix, ωiIs the ith order circle frequency.
Specifically, in the step (2), the matrix of curvature of the beam structure compliance matrix F according to rows is Fc，FcThe matrix of curvature by column is Fcc：
Figure BDA0001278171260000033
Figure BDA0001278171260000034
Figure BDA0001278171260000035
Figure BDA0001278171260000036
Wherein,
Figure BDA0001278171260000037
is FcThe value of the element, l, in the ith row and jth column of the matrixjThe average value of the distance between the measuring point j-1 and the measuring point j and the distance between the measuring point j and the measuring point j +1,
Figure BDA0001278171260000038
is FccThe value of the element, l, in the ith row and jth column of the matrixiThe average value of the distance from the measuring point i-1 to the measuring point i and the distance from the measuring point i to the measuring point i +1 is obtained.
Further, in the step (2), the curvature matrix F of the complianceccOr FcThe vector N is obtained by sequentially calculating the p norm of each column vectorp：
Np＝[Np(1) Np(2) L Np(n)]T
Figure BDA0001278171260000041
Wherein N isp(x) Is NpThe value of the xth element in the vector, p is 1 or 2, i.e. 1-norm or 2-norm, and other finite real numbers greater than 1, such as p is 1.5; n is the number of the measuring points.
Further, in the step (2), the norm difference index is used for carrying out structural damage positioning;
MFCCN1＝N1d-N1u
MFCCN2＝N2d-N2u
wherein the MFCCN1 and the MFCCN2 respectively represent 1-norm and 2-norm damage localization indexes, N1u、N1dRespectively representing the compliance curvature matrix from the undamaged state
Figure BDA0001278171260000042
And damage state compliance curvature matrix
Figure BDA0001278171260000043
Calculated 1-norm, N2u、N2dRespectively representing the compliance curvature matrix from the undamaged state
Figure BDA0001278171260000044
And damage state compliance curvature matrix
Figure BDA0001278171260000045
The calculated 2-norm, where the subscripts "u", "d" indicate the intact and damaged states, respectively.
Specifically, in the step (3), the node damage degree is calculated by using the following formula:
Figure BDA0001278171260000046
wherein N ispu(x)、Npd(x) Respectively representing the compliance curvature matrix p-norm of the x position before and after the beam structure is damaged.
Further, in the step (3), the node damage degree D is obtained through calculationn(x) Values less than 0 are set to 0.
Further, in the step (3), the unit damage degree is calculated by adopting the following formula:
Figure BDA0001278171260000047
wherein De(x) Degree of cell damage at x position, Dn(x) The x-position node damage degree.
The invention provides a beam structure damage degree calculation method based on the relative change of indexes before and after structural damage and the relationship between the node damage degree and the unit damage degree. The method can effectively position the damage of the beam structure under single-damage and multi-damage working conditions, and accurately identify the damage degree, and provides an effective new method for nondestructive detection and evaluation of the beam structure.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention.
FIG. 2 is a graph of the relationship between unit damage and node damage according to the present invention.
FIG. 3 is a diagram of a finite element model of a simply supported beam according to an embodiment of the present invention.
Fig. 4 is a damage localization diagram of the operating condition 1 mfccxmx index in the first embodiment of the present invention.
Fig. 5 is a diagram of the location of the damage of the indicator of the operating mode 1MFCCD according to the first embodiment of the present invention.
Fig. 6 is a damage location diagram of the indicator of the working condition 1MFCCN1 according to the first embodiment of the present invention.
Fig. 7 is a damage location diagram of the indicator 1MFCCN2 under the first operating condition in the embodiment of the present invention.
Fig. 8 is a damage localization diagram of the operating condition 2 mfccxmx index in the first embodiment of the present invention.
Fig. 9 is a diagram of the location of the damage of the indicator of the operating mode 2MFCCD according to the first embodiment of the present invention.
Fig. 10 is a damage location diagram of the indicator 2MFCCN1 under the first operating condition according to the embodiment of the present invention.
Fig. 11 is a damage location diagram of the indicator 2MFCCN2 under the first operating condition in the embodiment of the present invention.
Fig. 12 is a graph illustrating the damage level identification of the MFCCMX indicator under the operating condition 1 in the first embodiment of the present invention.
Fig. 13 is a graph illustrating the damage level identification of the MFCCD index under the working condition 1 according to the first embodiment of the present invention.
Fig. 14 is a graph illustrating the identification of the damage level of the indicator of 1MFCCN1 under the first operating condition in accordance with the embodiment of the present invention.
Fig. 15 is a graph illustrating the identification of the damage level of the indicator of the operating condition 1MFCCN2 according to the first embodiment of the present invention.
Fig. 16 is a graph illustrating the damage level identification of the MFCCMX indicator under the operating condition 2 in the first embodiment of the present invention.
Fig. 17 is a graph illustrating the damage level identification of the operating mode 2MFCCD indicator according to the first embodiment of the present invention.
Fig. 18 is a graph illustrating the identification of the damage level of the indicator 2MFCCN1 under the first operating condition in accordance with the embodiment of the present invention.
Fig. 19 is a graph illustrating the identification of the damage level of the indicator 2MFCCN2 under the first operating condition in accordance with the embodiment of the present invention.
FIG. 20 is a finite element model diagram of a three-span continuous beam according to a second embodiment of the present invention.
FIG. 21 is a diagram of the damage localization of the condition 3MFCCMX index in the second embodiment of the present invention.
Fig. 22 is a diagram of the location of the damage of the index of the working condition 3MFCCD in the second embodiment of the present invention.
Fig. 23 is a diagram of the damage location of the indicator of the working condition 3MFCCN1 in the second embodiment of the present invention.
FIG. 24 is a diagram illustrating the damage localization of the indicator 3MFCCN2 under the second embodiment of the present invention.
FIG. 25 is a diagram of the damage localization of the 4MFCCMX index under the second embodiment of the present invention.
Fig. 26 is a diagram of the location of the damage of the indicator of the operating condition 4MFCCD in the second embodiment of the present invention.
Fig. 27 is a damage location diagram of the indicator 4MFCCN1 under the second embodiment of the present invention.
FIG. 28 is a diagram illustrating the damage localization of the 4MFCCN2 indicator under the second embodiment of the present invention.
Fig. 29 is a recognition diagram of the damage degree of the operating condition 3 mfccxmx index in the second embodiment of the present invention.
Fig. 30 is a graph of identifying the damage degree of the indicator of the working condition 3MFCCD in the second embodiment of the present invention.
Fig. 31 is a graph illustrating the identification of the damage level of the indicator of the working condition 3MFCCN1 in the second embodiment of the present invention.
Fig. 32 is a graph illustrating the identification of the damage level of the indicator of the working condition 3MFCCN2 in the second embodiment of the present invention.
Fig. 33 is a graph of the damage level identification of the operating condition 4 mfccxmx index in the second embodiment of the present invention.
Fig. 34 is a graph illustrating the identification of the damage level of the operating condition 4MFCCD indicator in the second embodiment of the present invention.
Fig. 35 is a graph illustrating the identification of the damage level of the indicator of 4MFCCN1 under the second operating condition in accordance with the present invention.
FIG. 36 is a graph illustrating the identification of the damage level of the indicator 4MFCCN2 under the second embodiment of the present invention.
Fig. 37 is a graph illustrating the influence of the modal order of the 4MFCCN1 index on the localization of the damage in the second embodiment of the present invention.
Fig. 38 is a graph illustrating the influence of the modal order of the index of 4MFCCN1 on the identification of the damage level in the second embodiment of the present invention.
Fig. 39 is a diagram of the damage location of the operating condition 4MFCN1 indicator in the second embodiment of the present invention.
Fig. 40 is a diagram of the damage location of the operating condition 4MFCN2 indicator in the second embodiment of the present invention.
Fig. 41 is a graph illustrating identification of the damage level of the indicator of 4MFCN1 under the second operating condition according to the second embodiment of the present invention.
Fig. 42 is a graph illustrating the identification of the damage level of the indicator of 4MFCN2 under the second operating condition in accordance with the present invention.
Detailed Description
The present invention is further described with reference to the following drawings and examples, wherein like reference numerals refer to the same or similar elements throughout the different views unless otherwise specified.
Fig. 1 is a block flow diagram of a beam structure damage identification method of modal compliance curvature matrix norm according to the present invention, which specifically includes the following steps:
step 1: and respectively obtaining modal parameters before and after the beam structure is damaged through testing, and respectively calculating a flexibility matrix according to the frequency and the vibration mode.
Step 2: and (3) solving the curvature of the compliance matrix before and after the beam structure is damaged, then solving the norm of each column vector of the compliance curvature matrix in sequence, and carrying out structural damage positioning by using the norm difference.
And step 3: and calculating the damage degree of the beam structure node according to the relative change of the norm of the compliance curvature matrix before and after damage, and further calculating to obtain the unit damage degree.
In the step 1, the number of the measuring points of each span in the modal test before and after the damage of the beam structure is not less than 8, and the positions of the measuring points before and after the damage are arranged identically.
In the step 1, the modal order obtained by the test is not less than 3.
In step 1, the mode test adopts a measurable excitation method to directly measure the mode shape normalized with respect to the mass matrix, or adopts a method only measuring output and establishes the mass matrix through a finite element model of a beam structure, and after normalizing the mode shape to the mass matrix, a mode compliance matrix F expressed by frequency and mode shape can be obtained:
Figure BDA0001278171260000081
wherein phi is [ phi ]1,φ2,L,φm]Is a mode matrix, m is a mode order, phii＝[φi1φi2L φin]TIs the ith order mode vector, n is the number of measuring points,
Figure BDA0001278171260000089
as a diagonal matrix, ωiIs the ith order circle frequency.
In step 2, the beam structure flexibility matrix F is F according to the matrix of the row-solving curvaturec，FcThe matrix of curvature by column is Fcc：
Figure BDA0001278171260000082
Figure BDA0001278171260000083
Figure BDA0001278171260000084
Figure BDA0001278171260000085
Wherein,
Figure BDA0001278171260000086
is FcThe value of the element, l, in the ith row and jth column of the matrixjThe average value of the distance between the measuring point j-1 and the measuring point j and the distance between the measuring point j and the measuring point j +1,
Figure BDA0001278171260000087
is FccThe value of the element, l, in the ith row and jth column of the matrixiThe average value of the distance from the measuring point i-1 to the measuring point i and the distance from the measuring point i to the measuring point i +1 is obtained.
Pair compliance curvature matrix Fcc(or F)c) The vector N is obtained by sequentially calculating the p norm of each column vectorp：
Np＝[Np(1) Np(2) L Np(n)]T(6)
Figure BDA0001278171260000088
Wherein N isp(x) Is NpThe value of the xth element in the vector, p is 1 or 2, i.e. 1-norm or 2-norm, and other finite real numbers greater than 1, such as p is 1.5; n is the number of the measuring points.
Performing structural damage positioning by using the norm difference index;
MFCCN1＝N1d-N1u(8)
MFCCN2＝N2d-N2u(9)
wherein, MFCCN1 and MFCCN2 respectively represent 1-norm and 2-norm damage localization indexes, N1u、N1dRespectively representing the compliance curvature matrix from the undamaged state
Figure BDA0001278171260000091
And damage state compliance curvature matrix
Figure BDA0001278171260000092
Calculated 1-norm, N2u、N2dRespectively representing the compliance curvature matrix from the undamaged state
Figure BDA0001278171260000093
And damage state compliance curvature matrix
Figure BDA0001278171260000094
The calculated 2-norm, where the subscripts "u", "d" indicate the intact and damaged states, respectively.
If the maximum value or the diagonal element operation is taken for the flexibility curvature matrix difference delta before and after the damage, the modal flexibility difference curvature matrix indexes MFCCMX and MFCCD can be obtained:
Figure BDA0001278171260000095
MFCCMX＝max(|Δ|) (11)
MFCCD＝diag(Δ) (12)
where max (| Δ |) represents the maximum value for matrix | Δ | by column, and diag (Δ) represents taking diagonal elements in matrix Δ.
In step 3, for the flexural beam, the relationship between the structural vibration displacement w and the rigidity is as follows:
Figure BDA0001278171260000096
Figure BDA0001278171260000097
in the formula: m (x, t) represents the x-position bending moment at time t, EI (x) represents the x-position stiffness, qi(t) represents the modal coordinates, w (x, t) represents the x-position structural vibration displacement at time t, and subscripts "u" and "d" represent the undamaged and damaged states, respectively.
Suppose the node is damaged to a degree Dn(x) Then, there are:
EId(x)＝[1-Dn(x)]EIu(x) (15)
assuming that the damage has little effect on the modal distribution of the beam, it is considered
qiu(t)＝qid(t) (16)
Then the above formula can be solved:
Figure BDA0001278171260000101
in the formula, qiu(t) is time dependent, and to make the above constant, should:
Figure BDA0001278171260000102
namely:
Figure BDA0001278171260000103
because the vibration mode is directly used for damage identification, the damage degree can not be effectively reflected, the invention adopts the norm of the compliance curvature matrix to replace the curvature of the vibration mode, the node damage degree is calculated by using a formula (20), and when D is usedn(x)<Time 0Dn(x)＝0。
Figure BDA0001278171260000104
Wherein N ispu(x)、Npd(x) Respectively representing the compliance curvature matrix p-norm of the x position before and after the beam structure is damaged.
Assuming that the bending moment change before and after the structural damage is small, M is consideredu(x,t)＝Md(x, t), so:
Figure BDA0001278171260000105
the curvature calculated by the center difference method is a node value, which reflects the node damage degree, and the relationship between the node damage degree and the unit damage degree is shown in fig. 2, assuming that the damage degree of the middle unit is De(x) Degree of damage D of left and right units on both sidese(l)＝DeIf (r) is 0, the curvature curve of displacement caused by actual unit damage is shown as a dotted line in the graph, and there is a sudden change, and the sudden change cannot be considered in the numerical calculation, for example, the node damage degree value of the left node (node No. 2) of the middle unit is a comprehensive value of the damage degrees of the left and right units, and here, the average value of the two is assumed to be:
w″de2l+w″de2r＝2w″dn2(22)
wherein, w ″)de2lRepresents the displacement curvature, w ″, of the left unit of node 2 in the damaged statede2rRepresents the displacement curvature, w ″, of the right unit of the damaged state node 2dn2Representing the displacement curvature of the No. 2 node of the damage state.
From formula (21):
Figure BDA0001278171260000111
using NpInstead of the displacement curvature w ″, formula (22) is replaced by:
Figure BDA0001278171260000112
will De(l) Substituting 0 into the above formula to simplify the relationship between the unit damage degree and the node damage degree is as follows:
Figure BDA0001278171260000113
wherein De(x) The degree of cell damage.
For the MFCCMX index, respectively adopt
Figure BDA0001278171260000114
Instead of N in the formula (21)pu、NpdCalculating the node damage degree, and respectively adopting MFCCD indexes
Figure BDA0001278171260000115
Instead of N in the formula (21)pu、NpdComputing node impairmentsDegree of the disease.
The invention is described below with reference to specific engineering examples.
In the first embodiment, as shown in fig. 3, the beam is a simple beam, the span is 10m, and the beam is divided into 20 units (in the figure, the numbers in the circles in the upper row are the unit numbers, and the numbers in the lower row are the node numbers) equally, the cross-sectional dimension b × h is 300mm × 500mm, and the elastic modulus E is 3.25 × 104MPa, density 2500kg/m3. The damage of the unit is simulated by the reduction of the elastic modulus, and the damage working condition of the beam structure is shown in table 1:
TABLE 1 simply supported Beam Damage Condition
Figure BDA0001278171260000121
The specific implementation steps are as follows:
step 1: obtaining modal parameters before and after the damage of the three-span continuous beam through finite element model simulation analysis, and calculating a flexibility matrix F according to the formula (1) by the vertical frequency and the vibration mode of the first three ordersu、Fd。
Step 2: the results of each damage index are shown in fig. 4-11, and it can be seen from the graphs that for single-damage and multi-damage working conditions, the mfccm index has poor effect, the MFCCN2 index has best effect, the index value of the undamaged position is about 0, and the damage index can be correctly located.
And step 3: according to the relative change of the norm of the curvature matrix of the flexibility before and after damage, the damage degree of the beam structure nodes is calculated by the formula (21), and then the unit damage degree is calculated by the formula (25), as shown in fig. 12-19, it can be seen that except the damage degree identified by the edge unit 20, the indexes of the MFCCN1 and the MFCCN2 are slightly smaller, the damage degrees of other intermediate units are basically the same as the theoretical value, the result of the MFCCN1 index is slightly smaller than the theoretical value, the result of the MFCCN2 index is slightly larger than the theoretical value, and the damage degree identification effect is good. The MFCCMX and MFCCD index results are obviously larger than the actual damage degree, and the damage degree can not be accurately quantified.
Example two: as shown in FIG. 20, isA finite element model of a three-span continuous beam is characterized in that span arrangement is 10m +15m +10m, 1.0m divides a unit, 35 units in total and 36 nodes in total, (numbers in an upper row of circles in the figure are unit numbers, and numbers in a lower row are node numbers) the section size is b × h which is 300mm × 500mm, the elastic modulus of the material is E which is 3.25 × 104MPa, density 2500kg/m3. The damage of the unit is simulated by the reduction of the elastic modulus, and the damage working condition of the beam structure is shown in table 2:
TABLE 2 Damage Condition of three-span continuous Beam
Figure BDA0001278171260000131
The specific implementation steps are as follows:
step 1: obtaining modal parameters before and after the damage of the three-span continuous beam through finite element model simulation analysis, and calculating a flexibility matrix F according to the formula (1) by the vertical frequency and the vibration mode of the first three ordersu、Fd。
Step 2: calculating norm difference indexes by the compliance matrixes before and after damage according to the formulas (8) and (9) to carry out structural damage positioning, wherein the results of all damage indexes are shown in figures 21-28, and the figures show that all indexes can carry out damage positioning correctly under the single damage working condition; for the multi-damage working condition, the MFCCMX identifies 6 damage positions, and the other three indexes all correctly identify 5 damage positions.
And step 3: according to the relative change of the norm of the curvature matrix of the flexibility before and after the damage, the damage degree of the beam structure nodes is calculated by the formula (21), and then the unit damage degree is calculated by the formula (25), as shown in fig. 29-36, it can be seen that the damage degree cannot be correctly quantified by the indexes of MFCMX and MFCCD, the identified damage degree is obviously greater than the actual damage degree, the results of the indexes of MFCCN1 and MFCCN2 are similar, and the damage degree can be accurately identified.
The damage index is obtained by only adopting the first 3-order vertical bending mode calculation during the analysis, and the change condition of the performance of the damage index is analyzed when the damage index is constructed by adopting mode parameters with different orders under the working condition 4. Taking MFCCN1 as an example, the damage localization and damage degree identification results obtained by respectively adopting the first 1, 2, and 3-order modal analysis are respectively shown in fig. 37 and 38, and it can be seen that only three damages can be identified when the 1-order modal is used, and an abnormal peak exists in the damage degree identification result; when the 2-order mode is used, damage at four places can be identified, and the damage degree identification result is inaccurate; in the 3-order mode, five damages can be correctly identified and the damage degree can be correctly identified, so that the MFCCN1 index can normally identify the damages only by the 3-order mode and the modes above.
Using a compliance curvature matrix FcCorresponding indexes are MFCN1 and MFCN2, the damage positioning and damage degree identification are carried out on the working condition 4 in the front 3-order vertical bending mode, the result is shown in a graph from 39 to 42, and the result is basically the same as the indexes of MFCCN1 and MFCCN2, and the damage positioning and damage degree identification can be carried out correctly.
The above description is only two embodiments of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention are included in the scope of the present invention.

Claims (6)

1. A beam structure damage identification method of modal compliance curvature matrix norm is characterized by comprising the following steps:
(1) modal parameters before and after the beam structure is damaged are respectively obtained through testing, and a flexibility matrix is respectively calculated according to the frequency and the vibration mode;
the mode parameter test adopts a measurable excitation method to directly measure the mode shape normalized about the mass matrix, or adopts a method only measuring output and establishes the mass matrix through a finite element model of the beam structure, and after the mode shape is normalized to the mass matrix, a mode compliance matrix F expressed by the frequency and the mode shape can be obtained:
Figure FDA0002515407230000011
wherein phi is [ phi ]1,φ2,…,φm]Is a mode matrix, m is a mode order, phii＝[φi1φi2…φin]TIs the ith order mode vector, n is the number of measuring points,
Figure FDA0002515407230000012
as a diagonal matrix, ωiIs the ith order circle frequency;
(2) curvature of a compliance matrix before and after the beam structure is damaged is solved, then p-norm is solved for each column vector of the compliance curvature matrix in sequence, and the structure damage is positioned by using p-norm difference;
(3) calculating the damage degree of the beam structure node according to the relative change of the p norm of the compliance curvature matrix before and after damage, and further calculating to obtain the unit damage degree;
in the step (2), the beam structure flexibility matrix F is a matrix F for solving the curvature according to rowsc，FcThe matrix of curvature by column is Fcc：
Figure FDA0002515407230000013
Figure FDA0002515407230000021
Figure FDA0002515407230000022
Figure FDA0002515407230000023
Wherein,
Figure FDA0002515407230000024
is FcThe value of the element, l, in the ith row and jth column of the matrixjThe average value of the distance between the measuring point j-1 and the measuring point j and the distance between the measuring point j and the measuring point j +1,
Figure FDA0002515407230000025
is FccThe value of the element, l, in the ith row and jth column of the matrixiThe average value of the distance from the measuring point i-1 to the measuring point i and the distance from the measuring point i to the measuring point i +1；
In the step (2), a curvature matrix F of the flexibility is matchedccOr FcThe vector N is obtained by sequentially calculating the p norm of each column vectorp：
Np＝[Np(1) Np(2)…Np(n)]T
Figure FDA0002515407230000026
Wherein N isp(x) Is NpThe x-th element value in the vector, p is a real number not less than 1; n is the number of measuring points;
in the step (2), the norm difference index is used for carrying out structural damage positioning;
MFCCN1＝N1d-N1u
MFCCN2＝N2d-N2u
wherein the MFCCN1 and the MFCCN2 respectively represent 1-norm and 2-norm damage localization indexes, N1u、N1dRespectively representing the compliance curvature matrix from the undamaged state
Figure FDA0002515407230000027
And damage state compliance curvature matrix
Figure FDA0002515407230000028
Calculated 1-norm, N2u、N2dRespectively representing the compliance curvature matrix from the undamaged state
Figure FDA0002515407230000029
And damage state compliance curvature matrix
Figure FDA00025154072300000210
The calculated 2-norm, where the subscripts "u", "d" indicate the intact and damaged states, respectively.
2. The method of claim 1 for identifying damage to a beam structure by modal compliance curvature matrix norm, wherein: in the step (1), the number of the measuring points of each span is not less than 8 in the modal parameter test before and after the beam structure is damaged, and the positions of the measuring points before and after the damage are arranged identically.
3. The method of identifying damage to a beam structure by modal compliance curvature matrix norm as claimed in claim 2, wherein: in the step (1), the modal order obtained by the test is not less than 3.
4. The method of claim 1 for identifying damage to a beam structure by modal compliance curvature matrix norm, wherein: in the step (3), the node damage degree is calculated by adopting the following formula:
Figure FDA0002515407230000031
wherein N ispu(x)、Npd(x) Respectively representing the compliance curvature matrix p-norm of the x position before and after the beam structure is damaged.
5. The method of claim 4 for identifying modal compliance curvature matrix norm beam structure damage, comprising: in the step (3), the node damage degree D is obtained through calculationn(x) Values less than 0 are set to 0.
6. The method of claim 5 for identifying modal compliance curvature matrix norm beam structure damage, characterized by: in the step (3), the unit damage degree is calculated by adopting the following formula:
Figure FDA0002515407230000032
wherein De(x) Degree of cell damage at x position, Dn(x) The x-position node damage degree.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20130025073A (en) * 2011-09-01 2013-03-11 삼성전자주식회사 Flexible touch screen and beam projector having the same
CN104462788A (en) * 2014-11-21 2015-03-25 华中科技大学 Finite element model correcting method based on reverse substructures
CN106289947A (en) * 2016-08-31 2017-01-04 中国人民解放军军械工程学院 A kind of high-strength light girder construction damnification recognition method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20130025073A (en) * 2011-09-01 2013-03-11 삼성전자주식회사 Flexible touch screen and beam projector having the same
CN104462788A (en) * 2014-11-21 2015-03-25 华中科技大学 Finite element model correcting method based on reverse substructures
CN106289947A (en) * 2016-08-31 2017-01-04 中国人民解放军军械工程学院 A kind of high-strength light girder construction damnification recognition method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Structural damage detection using modal curvature and fuzzy logic;Chandrashekhar M 等;《Structural Health Monitoring》;20090430;第8卷(第4期);第267-282页 *
钢筋混凝土梁损伤诊断的振动模态分析方法;赵亚平;《中国博士学位论文全文数据库 工程科技Ⅱ辑》;20050915;第C038-19页 *

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