CN110487574B - Beam structure damage identification method based on inclination angle influence line curvature - Google Patents

Beam structure damage identification method based on inclination angle influence line curvature Download PDF

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CN110487574B
CN110487574B CN201910798847.1A CN201910798847A CN110487574B CN 110487574 B CN110487574 B CN 110487574B CN 201910798847 A CN201910798847 A CN 201910798847A CN 110487574 B CN110487574 B CN 110487574B
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damage
inclination angle
curvature
beam structure
influence line
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CN110487574A (en
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唐盛华
成鹏
张学兵
秦付倩
杨文轩
张佳奇
刘宇翔
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Xiangtan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0041—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress
    • G01M5/005—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress by means of external apparatus, e.g. test benches or portable test systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M99/00—Subject matter not provided for in other groups of this subclass
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M99/00—Subject matter not provided for in other groups of this subclass
    • G01M99/007—Subject matter not provided for in other groups of this subclass by applying a load, e.g. for resistance or wear testing

Abstract

The invention discloses a beam structure damage identification method based on inclination angle influence line curvature, which comprises the following steps: respectively applying moving loads to the measuring point positions of the beam structure before and after the beam structure is damaged to obtain an actually measured inclination angle influence line of an inclination angle testing position before and after the beam structure is damaged; calculating the curvature of the dip angle influence lines before and after damage, and carrying out damage positioning through the curvature difference of the dip angle influence lines; quantifying the damage degree through the relative change of the curvature of the inclination angle influence line before and after the beam structure is damaged; if the beam structure is a hyperstatic structure, acquiring inclination angle influence lines of a plurality of inclination angle test positions of the beam structure before and after damage to obtain the curvatures of the inclination angle influence lines of the plurality of inclination angle test positions of the beam structure before and after damage, and quantifying the damage degree based on the relative change of the sum of the absolute values of the curvatures of the inclination angle influence lines of the plurality of positions before and after damage. The method has low requirement on the number of the measuring points, saves the using amount of a monitoring sensor, can accurately position and quantify the damage of the beam structure, and is applied to the damage evaluation of the beam structure.

Description

Beam structure damage identification method based on inclination angle influence line curvature
Technical Field
The invention relates to the technical field of beam structure damage detection, in particular to a beam structure damage identification method based on inclination angle influence line curvature.
Background
In recent years, more and more old bridges are used in China, and the problems are increasingly obvious. Many existing bridges cannot meet functional requirements, and safety accidents such as bridge breakage and collapse occur sometimes, so that scholars in the field of civil engineering gradually realize the importance of health monitoring and safety assessment on bridge structures and research various damage identification technologies. Structural damage identification is an important component of a bridge structure health monitoring system, two major damage identification methods are mainly used at present, one is a damage identification method based on dynamic parameters, structural damage is judged mainly through changes of structural modes (vibration frequency and vibration mode), and the method has high requirements on the number of measuring points, the measurement precision of a sensor, a mode parameter identification method and the like. The other method is a damage identification method based on static parameters, the structural damage identification method based on the static parameters can effectively avoid the uncertain influences of quality, particularly damping and the like, and meanwhile, the structural damage identification technology based on the static parameters is widely researched because the existing measurement equipment and technology are advanced and mature and a quite accurate measurement value of a structure can be obtained at a lower cost.
The structural damage identification technology based on the static force parameter is mainly researched based on deflection, static force strain, support reaction force influence line indexes and the like, along with the progress of the tilt sensor technology, the change of a structural tilt angle curve before and after damage is expected to be applied to structural damage identification, and at present, relevant literature reports about tilt angle damage identification are rarely seen.
Disclosure of Invention
In order to solve the technical problems, the invention provides a beam structure damage identification method based on inclination angle influence line curvature, which is simple in algorithm and low in cost.
The technical scheme for solving the problems is as follows: a beam structure damage identification method based on inclination angle influence line curvature is characterized by comprising the following steps:
(1) respectively applying moving loads to the measuring point positions of the beam structure before and after the beam structure is damaged to obtain an actually measured inclination angle influence line of an inclination angle testing position before and after the beam structure is damaged;
(2) curvature of the inclination angle influence lines before and after the beam structure is damaged is calculated, and damage positioning is carried out through the curvature difference of the inclination angle influence lines;
(3) quantifying the damage degree through the relative change of the curvature of the inclination angle influence line before and after the beam structure is damaged;
(4) if the beam structure is a hyperstatic structure, the steps (1) to (2) are repeated for multiple times to obtain the inclination angle influence line curvatures of a plurality of inclination angle test positions of the beam structure before and after damage, the damage is positioned based on the sum of the inclination angle influence line curvature absolute value differences, and the damage degree is quantified based on the relative change of the sum of the inclination angle influence line curvature absolute values.
In the method for identifying the beam structure damage based on the inclination angle influence line curvature, in the step (2), the inclination angle influence line curvature θ ″ is obtained by central difference calculation:
Figure BDA0002181732670000021
wherein, the subscript i is a measuring point number, theta ″)iThe curvature of a dip angle influence line of a measuring point i is shown, epsilon is the average value of the distance between the measuring point i-1 and the measuring point i and the distance between the measuring point i and a measuring point i +1, and theta isiThe inclination angle of the test position when the load acts on the point i.
In the above beam structure damage identification method based on the curvature of the inclination influence line, in the step (2), the differential damage positioning index DI of the curvature of the inclination influence line is:
Figure BDA0002181732670000022
wherein, theta ″)iu、θ″idThe curvature of a test position dip angle influence line before and after the damage of the ith test point structure is acted by load, n is the number of test points, the number 1 of test points is arranged at one end of the beam structure, the number n of test points is arranged at the other end of the beam structure, the number of the test points is continuous and increases from 1 to n, and i is more than or equal to 2 and less than or equal to n-1.
In the beam structure damage identification method based on the inclination angle influence line curvature, in the step (3), the quantitative index D of the structure damage degreeeThe calculation method comprises the following steps:
De＝[0 De2 … Dei … De(n-1) 0]；
wherein D iseiThe structural damage degree identified for the ith measuring point;
for the structure intermediate unit, the damage degree calculation method comprises the following steps:
Figure BDA0002181732670000031
for the side unit of the structure, if the corner is restrained, the damage degree is as follows:
Figure BDA0002181732670000032
for the side unit of the structure, if the corner is not constrained, when the dip angle test position is the fulcrum test point of the damaged side unit, the damage degree of the damaged unit is still as follows:
Figure BDA0002181732670000033
otherwise:
Figure BDA0002181732670000034
according to the beam structure damage identification method based on the inclination angle influence line curvature, in the step (4), m inclination angle test positions are selected, and the inclination angle influence line curvature absolute value difference delta theta' before and after k test position structure damagekIs as follows; delta theta ″)k＝|θ″dk|-|θ″uk|＝[0 |θ″2dk|-|θ″2uk| … |θ″idk|-|θ″iuk| … |θ″(n-1)dk|-|θ″(n-1)uk| 0]；
Wherein, theta ″)uk、θ″dkThe curvature of the line, theta ″, is affected by the dip angle before and after the structural damage of the k test positioniuk、θ″idkRespectively measuring the curvature of the inclination angle influence line before and after the structural damage of the k test position of the ith test point under the action of load, wherein m is the number of the k test positions, m is more than or equal to 2, and k is more than or equal to 1 and less than or equal to m;
in the step (4), the dip angle influence line curvature absolute value differences of m dip angle test positions are summed to obtain a hyperstatic structure damage positioning index DIa：
Figure BDA0002181732670000041
In the step (4), the hyperstatic structure damage degree quantitative index DeaThe calculation method comprises the following steps:
Dea＝[0 Dea2 … Deai … Dea(n-1) 0]；
wherein D iseaiIdentifying the structural damage degree of the ith measuring point of the statically indeterminate beam structure;
for the structure intermediate unit, the damage degree calculation method comprises the following steps:
Figure BDA0002181732670000042
for the structural edge unit, if the corner is restrained, the damage degree is as follows:
Figure BDA0002181732670000043
for the side unit of the structure, if the corner is not constrained, when the dip angle test position is the fulcrum test point of the damaged side unit, the damage degree of the damaged unit is still as follows:
Figure BDA0002181732670000051
otherwise:
Figure BDA0002181732670000052
in the beam structure damage identification method based on the inclination angle influence line curvature, in the step (4), when the inclination angle test position is positioned on a test point of a certain damage unit, the damage degree value of the adjacent test point is obtained.
According to the beam structure damage identification method based on the inclination angle influence line curvature, in the steps (1) and (4), the positions of measuring points for the inclination angle influence line test before and after the structure damage are arranged the same, and the number of the measuring points of the influence line is not less than 6 per span.
The invention has the beneficial effects that: the method applies moving load to the beam structure before and after damage to obtain the difference of the curvature of the incidence influence line before and after damage of each measuring point of the beam structure, carries out damage positioning, simultaneously establishes an explicit expression for calculating the damage degree according to the curvature of the incidence influence line before and after damage of the structure, and can directly calculate the damage degree according to the curvature of the incidence influence line. And by adopting the simple beam, cantilever beam and three-span continuous beam calculation examples, various damage working conditions are considered, the application value of the inclination angle influence line curvature index in beam structure damage identification is verified, and an effective new method is provided for beam structure damage positioning and quantification.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention.
FIG. 2 is a diagram of a simple beam structure model according to the present invention.
FIG. 3 is a bending moment diagram of the simple support beam unit bending moment acting on the position b.
FIG. 4 is a view of the concentrated load action bending moment of the simply supported beam of the present invention.
FIG. 5 is a schematic view of the concentrated load effect of the three-span continuous beam.
FIG. 6 is a graph of the influence line curvature of the inclination angle of the three-span continuous beam 1# to 3# supports.
FIG. 7 is a schematic finite element model diagram of a simply supported beam according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of a positioning index DI for the impact line damage of the inclination angle of the simply supported beam measuring point 1 in the first embodiment of the present invention.
FIG. 9 shows the line loss of the simply supported beam measuring point 1 due to the inclination angleInjury quantitative index DeSchematic representation of (a).
Fig. 10 is a schematic diagram of a positioning index DI of the impact line damage of the inclination angle of the simply supported beam measuring point 10 in the first embodiment of the present invention.
FIG. 11 is a quantitative indicator D of the damage degree of the inclination angle influence line of the simply supported beam measuring point 10 in the first embodiment of the present inventioneSchematic representation of (a).
FIG. 12 is a graph of the curvature of the inclination angle influence line of the simply supported beam measuring points 1 and 10 according to the first embodiment of the present invention.
Fig. 13 is a schematic diagram of a positioning index DI of the impact line damage of the inclination angle of the simply supported beam measuring point 21 in the first embodiment of the present invention.
FIG. 14 is a diagram of a quantitative indicator D of the damage degree of the dip-angle influence line of the simply supported beam measuring point 21 in the first embodiment of the present inventioneSchematic representation of (a).
FIG. 15 is a diagram of a finite element model of a second cantilever according to an embodiment of the present invention.
Fig. 16 is a schematic diagram of a cantilever beam damage localization index DI according to a second embodiment of the present invention.
FIG. 17 is a quantitative index D of the beam damage degree of the cantilever according to the second embodiment of the present inventioneSchematic representation of (a).
FIG. 18 is a finite element model diagram of a three-span continuous beam according to an embodiment of the present invention.
FIG. 19 is a schematic diagram of a measurement point 1 tilt angle influence line damage positioning index DI in the third embodiment of the present invention.
FIG. 20 is a schematic diagram of a measurement point 11 tilt angle influence line damage location index DI in the third embodiment of the present invention.
FIG. 21 is a schematic diagram of a measurement point 26 inclination angle influence line damage positioning index DI in the third embodiment of the present invention.
FIG. 22 is a schematic diagram of a measurement point 36 inclination angle influence line damage localization index DI in the third embodiment of the present invention.
FIG. 23 shows the damage localization index DI under working condition 1 in the third embodiment of the present inventionaSchematic representation of (a).
FIG. 24 is a quantitative index D of damage degree of the measuring point 1 inclination angle influence line in the third embodiment of the present inventioneSchematic representation of (a).
FIG. 25 is a graph showing the damage degree of the measuring point 11 at the dip angle influence line in the third embodiment of the present inventionQuantity index DeSchematic representation of (a).
FIG. 26 is a quantitative index D of damage degree of the measuring point 26 inclination angle influence line in the third embodiment of the present inventioneSchematic representation of (a).
FIG. 27 is a quantitative index D of the damage degree of the measuring point 36 inclination angle influence line in the third embodiment of the present inventioneSchematic representation of (a).
FIG. 28 is a graph showing a damage degree quantitative index D obtained by superimposing indexes 1# -4 # in the third embodiment of the present inventioneaSchematic representation of (a).
FIG. 29 is a graph showing a damage degree quantitative index D obtained by superimposing No. 1, No. 2 and No. 4 in the third embodiment of the present inventioneaSchematic representation of (a).
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.
As shown in fig. 1, a method for identifying damage to a beam structure based on a curvature of an inclination influence line includes the following steps:
1. and respectively applying moving loads to the measuring point positions of the beam structure before and after the beam structure is damaged to obtain an actually measured inclination angle influence line of the inclination angle testing position before and after the beam structure is damaged.
2. And (4) solving the curvature of the inclination angle influence line before and after the beam structure is damaged, and carrying out damage positioning through the curvature difference of the inclination angle influence line.
3. And quantifying the damage degree through the relative change of the curvature of the inclination angle influence line before and after the beam structure is damaged.
4. If the beam structure is a hyperstatic structure, the steps (1) to (2) are repeated for multiple times to obtain the inclination angle influence line curvatures of a plurality of inclination angle test positions of the beam structure before and after damage, damage positioning is carried out based on the sum of the inclination angle influence line curvature absolute value differences, and degree quantification is carried out based on the relative change of the sum of the inclination angle influence line curvature absolute values.
Applying the step 1, taking a simple supported beam as an example, as shown in a structural model figure 2, wherein the span of the simple supported beam is L, A, B are two end points of the simple supported beam, the distance between a damage position and a left end A is a, the distance between each measuring point is epsilon, and the rigidity of an undamaged structure isEI, the rigidity of the damaged cell is EId. The inclination angle influence line is at a position b (b is less than or equal to a) away from the left end A, and the bending moment when the unit bending moment M is 1 and acts at the position is (as shown in figure 3):
Figure BDA0002181732670000081
Figure BDA0002181732670000082
when the unit bending moment M is 1 and the length from the left end A is b, x belongs to [0, b ∈]In the process, the distance from the left end point A of the simply supported beam is a bending moment at the position of x;
Figure BDA0002181732670000083
indicates that x ∈ (b, L) when the unit bending moment M ═ 1 acts at a position b away from the left end a by a length]In the process, the distance from the left end point A of the simply supported beam is a bending moment at the position of x; x represents the distance from the left end point A of the simply supported beam;
the load P acts at a distance A from the left end by a length of
Figure BDA0002181732670000084
The bending moment at position is:
Figure BDA0002181732670000085
M1(x) Indicating that the load P acts over a length A from the left end
Figure BDA0002181732670000086
In the case of the position, the position of the user,
Figure BDA0002181732670000087
in the process, the distance from the left end point A of the simply supported beam is a bending moment at the position of x; m2(x) Indicating that the load P acts over a length A from the left end
Figure BDA0002181732670000088
In the case of the position, the position of the user,
Figure BDA0002181732670000089
in the process, the distance from the left end point A of the simply supported beam is a bending moment at the position of x;
the inclination influence line can be obtained by multiplying the concentrated load P from the left end to the right end (see FIG. 4).
When not damaged, when the moving load P is at [0, b ]]In intervals, i.e.
Figure BDA00021817326700000810
When the angle of inclination at the position b from the left end A
Figure BDA00021817326700000811
Comprises the following steps:
Figure BDA0002181732670000091
when the moving load P is located at (b, L)]In the interval, the inclination angle influence line at the position b away from the left end A
Figure BDA0002181732670000092
Comprises the following steps:
Figure BDA0002181732670000093
in the formula, the subscript "u" represents the state of intact structure.
When the structure is damaged, when the moving load P is positioned at [0, b ]]In the interval, the inclination angle influence line at the position b away from the left end A
Figure BDA0002181732670000094
Comprises the following steps:
Figure BDA0002181732670000095
when the moving load P is located at (b, a)]In the interval, the inclination angle influence line at the position b away from the left end A
Figure BDA0002181732670000096
Comprises the following steps:
Figure BDA0002181732670000097
when the moving load P is located at [ a + epsilon, L]In the interval, the inclination angle influence line at the position b away from the left end A
Figure BDA0002181732670000098
Comprises the following steps:
Figure BDA0002181732670000099
in the formula, subscript "d" represents the structural damage state.
Applying the step 2, the curvature of the inclination angle influence line in the undamaged state obtained by the formula (4) is as follows:
Figure BDA0002181732670000101
for the damage state, when loads P act on a left measuring point i-2, a right measuring point i, a left measuring point i +1 and a measuring point i +1 which is away from a measuring point epsilon of an damage position, the inclination angle influence lines of the position b are respectively (assuming that b is less than or equal to a-epsilon):
θ(i-2)d＝θdL(a-ε) (9)
θ(i-1)d＝θdL(a) (10)
θid＝θdL(a+ε) (11)
θ(i+1)d＝θdL(a+2ε) (12)
the curvatures of the dip angle influence lines of the damage positions i-1 and i measuring points can be calculated by adopting a central difference method, and are respectively as follows:
Figure BDA0002181732670000102
Figure BDA0002181732670000103
the curvature of the influence line of the inclination angle of the measuring point i-1 and i under the action of the load before damage is as follows:
Figure BDA0002181732670000104
Figure BDA0002181732670000105
as can be seen from the above derivation, EI is obtained when the cell between the i-1 and i-test points is not damageddWhen equal to EI, theta ″)(i-1)u＝θ″(i-1)d、θ″iu＝θ″idThat is, theoretically, the difference of the curvature of the inclination angle influence line before and after the damage is 0 at the undamaged unit, and when the structure is damaged, theta ″, is(i-1)u≠θ″(i-1)d、θ″iu≠θ″idTherefore, the damage positioning can be carried out through the difference of the curvature of the incidence influence line before and after the damage, and the DI calculation method of the damage positioning index is as follows:
DI＝[DI1 DI2 … DIi … DIn-1 DIn] (17)
DIi＝θ″id-θ″iu (18)
in the formula: n is the number of measuring points, the curvature of the measuring points 1 and n at the supporting position of the side of the beam structure can not be calculated, and DI is taken1＝DIn＝0。
Application step 3:
(1) when b is less than or equal to a-epsilon
For the right unit damage, in this case, a is L-epsilon, the curvature of the inclination angle influence line at the point i-1 before and after the structural damage is obtained, and the curvatures are respectively represented by the following formulas (15) and (13):
Figure BDA0002181732670000111
Figure BDA0002181732670000112
by substituting formula (19) for formula (20):
Figure BDA0002181732670000113
therefore, the damage level of the cell can be obtained as follows:
Figure BDA0002181732670000114
for intermediate unit damage, where a < L- ε, one can see from equations (15), (13) and (16), (14):
Figure BDA0002181732670000115
Figure BDA0002181732670000116
therefore, the damage level of the cell can be obtained as follows:
Figure BDA0002181732670000117
(2) when b is a
The incidence influence line of the damage state is divided into two sections, and the moving load P is positioned at [0, b ]]In the interval, the inclination angle influence line at the position b away from the left end A is
Figure BDA0002181732670000121
The moving load P is located at (b, L)]In the interval, the inclination angle influence line at the position b away from the left end A is
Figure BDA0002181732670000122
The calculation method comprises the following steps:
Figure BDA0002181732670000123
Figure BDA0002181732670000124
the curvature of the influence line of the inclination angle of the measuring point i-1 and i under the action of the load before damage is as follows:
Figure BDA0002181732670000125
Figure BDA0002181732670000126
as can be seen by comparing formulas (15) and (16), when b ═ a, θ ″ ", the product is obtained(i-1)uDifferent, θ ″)iuThe same is true.
The curvature of the incidence influence line of the measuring points i-1 and i under the load action of the damage state is as follows:
Figure BDA0002181732670000127
Figure BDA0002181732670000128
the following equations (29) and (31) can be obtained:
Figure BDA0002181732670000129
therefore, the damage level of the cell can be obtained as follows:
Figure BDA00021817326700001210
from equations (28) and (30), the damage degree can be obtained:
Figure BDA0002181732670000131
as can be seen, θ ″)(i-1)uAnd theta ″)(i-1)dThe relation of (a) is related to the specific values of a, L and epsilon, and a general conclusion cannot be obtained, namely the conclusion of the formula cannot be popularized and used in other structures such as cantilever beams and continuous beams. Therefore, when the inclination angle observation position is just positioned at the measuring point of the damage unit, the damage identification result of the measuring point beside the inclination angle observation position can be taken.
As for the side unit damage, a is 0, and as is clear from equations (29) and (31), the calculation formula of the degree of damage is also equation (33).
Applying the step 4, regarding the hyperstatic structure, taking a three-span continuous beam as an example, as shown in fig. 5, 1#, 2#, and 3# support position inclination angle influence line curvature as shown in fig. 6, an inclination angle influence line curvature curve will have a zero point, so that the damage quantitative formula cannot accurately identify the damage degree at the zero point, and a sudden change can occur, but the positions of the two inclination angle influence line curvature zero points are different, so that the problem that the damage at the inclination angle influence line curvature zero points cannot be identified by overlapping the inclination angle influence line curvature absolute values at multiple positions is considered. The acquired inclination angle test positions are preferably spaced at proper distances, the data of the inclination angle influence lines are as large as possible, and the curvature superposition of the inclination angle influence lines at all branch points of the continuous beam structure can be acquired for carrying out damage identification.
Selecting m dip angle test positions, wherein the absolute value difference of the curvature of the dip angle influence line before and after the structure of the k test positions is;
δθ″k＝|θ″dk|-|θ″uk|＝[0 |θ″2dk|-|θ″2uk| … |θ″idk|-|θ″iuk| … |θ″(n-1)dk|-|θ″(n-1)uk| 0] (35)
wherein, theta ″)uk、θ″dkThe curvature of the line, theta ″, is affected by the dip angle before and after the structural damage of the k test positioniuk、θ″idkThe curvature of the inclination angle influence line before and after the structure of the test position k of the ith test point is damaged by the load, m is the number of the test positions of the inclination angle, m is more than or equal to 2, and k is more than or equal to 1 and less than or equal to m.
The absolute value differences of the curvature of the inclination angle influence lines of the m inclination angle test positions are summed to obtain a hyperstatic structure damage positioning index DIa：
Figure BDA0002181732670000132
Hyperstatic structure damage degree quantitative index DeaThe calculation method comprises the following steps:
Dea＝[0 Dea2 … Deai … Dea(n-1) 0] (37)
wherein D iseaiAnd identifying the structural damage degree of the ith measuring point of the statically indeterminate beam structure.
For the structure intermediate unit, the damage degree calculation method comprises the following steps:
Figure BDA0002181732670000141
for the structural edge unit, if the corner is constrained, if the corner is fixed and supported, the damage degree is as follows:
Figure BDA0002181732670000142
for the side unit of the structure, if the corner is not constrained, such as a simple support end and a cantilever end, when the inclination angle test position is a fulcrum test point of the damaged side unit, the damage degree of the damaged unit is still as follows:
Figure BDA0002181732670000143
otherwise:
Figure BDA0002181732670000144
in the steps 1 and 4, the positions of measuring points for the inclination angle influence line test before and after the structural damage are arranged the same, and the number of the measuring points of the influence line is not less than 6 per span.
The first embodiment is as follows: referring to fig. 7, the span of the simply supported beam is 100cm, and 5cm is divided into a unit, 20 units and 21 measuring points (in the figure, the numbers in the circles at the upper row are the unit numbers, and the numbers at the lower row are the measuring point numbers). The cross-section dimension of the plate is 4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 103MPa, Poisson's ratio of 0.37, density of 1200kg/m3。
Damage in an actual engineered structure, such as crack initiation, material corrosion, or a decrease in elastic modulus, typically only causes a large change in the stiffness of the structure, with little effect on the mass of the structure. Therefore, in finite element calculations, it is assumed that structural element damage only causes a decrease in element stiffness, and not a change in element mass. Damage to the cell is simulated by a decrease in the modulus of elasticity. Beam structure models were built using ANSYS software beam3 beam cells. Taking a multi-unit damage condition as an example, consider that the edge unit 1 and the midspan unit 10 are damaged at different degrees at the same time, and the damage condition is shown in table 1.
TABLE 1 simply supported Beam Multi-Damage Condition
Figure BDA0002181732670000151
The specific implementation steps are as follows:
step 1: and respectively applying 1kN moving loads to the simply supported beams before and after the damage to obtain actually measured inclination angle influence lines before and after the damage of the simply supported beams, wherein measuring points 1, 10 and 21 are selected as inclination angle test positions.
Step 2: the curvature of the inclination angle influence lines before and after the beam structure is damaged is calculated, damage positioning is carried out through the inclination angle influence line curvature difference, as shown in fig. 8, 10 and 13, results show that obvious peak values appear at the units 1 and 10, DI at other undamaged positions is 0, all damage can be identified through the index, and the influence line of the inclination angle of the measuring point 1 has the most obvious effect of positioning the damage of the unit 1.
And step 3: the damage degree is quantified through the relative change of the inclination angle influence line curvature before and after the beam structure is damaged, and the damage degree index D of the multi-damage working condition 1-2eThe recognition effect is as shown in fig. 9, fig. 11 and fig. 14, except for fig. 11, the index can accurately quantify the damage degree, the recognized damage degree is very close to the actual damage degree, the damage degree recognized by the measuring point 10 in fig. 11 is incorrect, and the damage degree recognized by other measuring points is close to the theoretical value, because the measuring point 10 is the left measuring point of the damage unit 10, the curvature of the inclination angle influence line of the measuring points 1 and 10 is as shown in fig. 12, it can be seen that the curvature curve of the inclination angle influence line of the measuring point 10 has a sudden change at the position of the measuring point 10, so the measuring point can not correctly recognize the damage degree, and the recognition result of the side measuring point 11 can be taken. Therefore, the damage degree of the simply supported beam can be accurately identified by the index.
Example two: referring to fig. 15, the span of the cantilever beam is 100cm, and 5cm is divided into a unit, 20 units and 21 measuring points (in the figure, the numbers in the circles at the upper row are the unit numbers, and the numbers at the lower row are the measuring point numbers). The cross-section dimension of the plate is 4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 103MPa, Poisson's ratio of 0.37, density of 1200kg/m3。
Considering that damage of different degrees commonly occurs at three positions of the fixed branch end unit 1, the midspan unit 10 and the free end unit 20, the damage working condition is shown in table 2.
TABLE 2 cantilever Multi-Damage Condition
Figure BDA0002181732670000161
The specific implementation steps are as follows:
step 1: and respectively applying 1kN moving loads to the cantilever beams before and after the damage to obtain actual measurement inclination angle influence lines before and after the damage of the cantilever beams, and selecting a cantilever beam measuring point 21 at an inclination angle test position.
Step 2: curvature of inclination angle influence lines before and after beam structure damage is solved, damage positioning is carried out through inclination angle influence line curvature difference, damage positioning indexes DI are shown in figure 16, peak values of unequal degrees appear in the unit 1, the unit 10 and the unit 20, damage positions of multiple damages can be accurately identified through the indexes, and no peak value exists.
And step 3: the damage degree is quantified through the relative change of the curvature of the inclination angle influence line before and after the damage of the beam structure, and a damage quantitative index DeThe recognition effect is as shown in fig. 17, and not only can it be judged that there are three locations where damage occurs, but also the recognized damage degree is close to the actual damage.
Example three: referring to fig. 18, the span diameter of the three-span continuous beam is arranged to be 100+150+100cm, and 10cm is divided into a unit, 35 units and 36 measuring points (in the figure, the numbers in the upper row of circles are the unit numbers, and the numbers in the lower row are the support numbers). The cross-section dimension of the plate is 4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 103MPa, Poisson's ratio of 0.37, density of 1200kg/m3。
The unit 7 is located near the point of 0 span bending moment under the action of uniformly distributed load, the unit 18 is a middle span middle unit, the unit 26 is a third span maximum negative bending moment unit, and the damage working conditions are shown in the table 3.
The specific implementation steps are as follows:
step 1: the continuous beam is of a statically indeterminate structure, so that the inclination angle influence line of each fulcrum section position is analyzed, the load is shifted to be 1kN, and the actually measured inclination angle influence line before and after damage of each fulcrum section position of the continuous beam is obtained.
TABLE 3 Damage Condition of three-span continuous Beam
Figure BDA0002181732670000171
Step 2: the curvature of the inclination angle influence line before and after the beam structure is damaged is calculated, the damage is positioned by summing the absolute value differences of the curvatures of the inclination angle influence lines, and the damage positioning index DI identification results of all the positions of the working condition 1 are shown in figures 19-22, so that the occurrence of the damage can be identifiedIndex DI after three lesions, superimposedaSee FIG. 23, where DI is seenaThe damage positioning effect of the index is better than that of the DI index, and the peak values of three damage positions are more obvious.
And step 3: the damage degree is quantified through the absolute value and the relative change of the curvature of the inclination angle influence line before and after the beam structure is damaged, and the damage degree quantitative index D of each position of the working condition 1eThe identification results are shown in FIGS. 24-27, all of which have abnormal peak interference, and the quantitative result of the damage degree is not very accurate, which affects the identification effect of the damage degree, and the indexes D after adding 1# -4 #, are addedeaThe recognition result is as shown in FIG. 28, the larger value is only at the damage position, the recognition result is close to the actual damage degree, the damage recognition result of the unit 26 is slightly larger, because the inclination angle of the 3# position affects the damage recognition of the line to the measuring point 26 (located at the left measuring point of the damage unit), if the 3# position is removed, only 1#, 2# and 4# are added, the damage degree D is addedeaThe identification result is shown in fig. 29, and the damage degree is identified more accurately, so that inclination angle influence lines at several positions need to be tested more for hyperstatic structures such as continuous beams, and then the inclination angle influence lines at proper positions are selected for superposition processing, so that the influence of the curvature zero point of the inclination angle influence lines is avoided, and the damage is better positioned and quantified.
The above description is only 3 embodiments of the present invention, and all equivalent changes and modifications made in the claims of the present invention are included in the scope of the present invention.

Claims (3)

1. A beam structure damage identification method based on inclination angle influence line curvature is characterized by comprising the following steps:
(1) respectively applying moving loads to the measuring point positions of the beam structure before and after the beam structure is damaged to obtain an actually measured inclination angle influence line of an inclination angle testing position before and after the beam structure is damaged;
(2) curvature of the inclination angle influence lines before and after the beam structure is damaged is calculated, and damage positioning is carried out through the curvature difference of the inclination angle influence lines;
in the step (2), the inclination angle influence line curvature theta' is obtained by central difference calculation:
Figure FDA0002825048410000011
wherein, the subscript i is a measuring point number, theta ″)iThe curvature of a dip angle influence line of a measuring point i is shown, epsilon is the average value of the distance between the measuring point i-1 and the measuring point i and the distance between the measuring point i and a measuring point i +1, and theta isiThe inclination angle of the test position when the load acts on the i test point is shown;
the dip angle influence line curvature difference damage positioning index DI is as follows:
Figure FDA0002825048410000012
wherein, theta ″)iu、θ″idThe curvature of a test position dip angle influence line before and after the damage of the ith test point structure is acted by load, n is the number of test points, the number 1 of test points is arranged at one end of the beam structure, the number n of test points is arranged at the other end of the beam structure, the number of the test points is continuous and increases from 1 to n, and i is more than or equal to 2 and less than or equal to n-1;
(3) quantifying the damage degree through the relative change of the curvature of the inclination angle influence line before and after the beam structure is damaged;
in the step (3), a quantitative index D of the degree of structural damageeThe calculation method comprises the following steps:
De＝[0 De2…Dei…De(n-1) 0]；
wherein D iseiThe structural damage degree identified for the ith measuring point;
for the structure intermediate unit, the damage degree calculation method comprises the following steps:
Figure FDA0002825048410000021
for the side unit of the structure, if the corner is restrained, the damage degree is as follows:
Figure FDA0002825048410000022
for the side unit of the structure, if the corner is not constrained, when the dip angle test position is the fulcrum test point of the damaged side unit, the damage degree of the damaged unit is still as follows:
Figure FDA0002825048410000023
otherwise:
Figure FDA0002825048410000024
(4) if the beam structure is a hyperstatic structure, the steps (1) to (2) are repeated for multiple times to obtain the inclination angle influence line curvatures of a plurality of inclination angle test positions of the beam structure before and after damage, the damage is positioned based on the sum of the inclination angle influence line curvature absolute value differences, and the damage degree is quantified based on the relative change of the sum of the inclination angle influence line curvature absolute values;
in the step (4), m dip angle test positions are selected, and the dip angle influence line curvature absolute value difference delta theta' before and after the k test position structure is damagedkIs as follows;
δθ″k＝|θ″dk|-|θ″uk|＝[0 |θ″2dk|-|θ″2uk|…|θ″idk|-|θ″iuk|…|θ″(n-1)dk|-|θ″(n-1)uk| 0]；
wherein, theta ″)uk、θ″dkThe curvature of the line, theta ″, is affected by the dip angle before and after the structural damage of the k test positioniuk、θ″idkRespectively measuring the curvature of the inclination angle influence line before and after the structural damage of the k test position of the ith test point under the action of load, wherein m is the number of the k test positions, m is more than or equal to 2, and k is more than or equal to 1 and less than or equal to m;
in the step (4), the dip angle influence line curvature absolute value differences of m dip angle test positions are summed to obtain a hyperstatic structure damage positioning index DIa：
Figure FDA0002825048410000031
In the step (4), the hyperstatic structure damage degree quantitative index DeaThe calculation method comprises the following steps:
Dea＝[0 Dea2…Deai…Dea(n-1) 0]；
wherein D iseaiIdentifying the structural damage degree of the ith measuring point of the statically indeterminate beam structure;
for the structure intermediate unit, the damage degree calculation method comprises the following steps:
Figure FDA0002825048410000032
for the structural edge unit, if the corner is restrained, the damage degree is as follows:
Figure FDA0002825048410000033
for the side unit of the structure, if the corner is not constrained, when the dip angle test position is the fulcrum test point of the damaged side unit, the damage degree of the damaged unit is still as follows:
Figure FDA0002825048410000034
otherwise:
Figure FDA0002825048410000041
2. the method for identifying beam structure damage based on inclination angle influence line curvature as claimed in claim 1, wherein: in the step (4), when the inclination angle test position is on a test point of a certain damage unit, the damage degree value of the adjacent test point is taken.
3. The method for identifying beam structure damage based on inclination angle influence line curvature as claimed in claim 1, wherein: in the steps (1) and (4), the positions of measuring points for the inclination angle influence line test before and after the structural damage are arranged the same, and the number of the measuring points of the influence line is not less than 6 per span.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104750926A (en) * 2015-03-27 2015-07-01 东南大学 Variable cross-section beam damage identification method based on node curvature and wavelet analysis
CN106897510A (en) * 2017-02-16 2017-06-27 西南交通大学 A kind of bridge structure 3-D seismics vulnerability analysis method
CN107085037A (en) * 2017-04-25 2017-08-22 湘潭大学 The vibration shape weights the girder construction damnification recognition method of Modal Flexibility
CN109543303A (en) * 2018-11-22 2019-03-29 华北水利水电大学 A method of the Damage Assessment Method to be perturbed based on class curvature of the flexibility difference matrix and frequency
CN106896156B (en) * 2017-04-25 2019-06-14 湘潭大学 The girder construction damnification recognition method of uniform load face curvature difference by cross

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106897543B (en) * 2017-04-25 2020-07-28 湘潭大学 Beam structure damage identification method of modal compliance curvature matrix norm
CN107246035B (en) * 2017-07-19 2018-07-17 交通运输部公路科学研究所 A kind of main pier concrete pile foundation breakdown diagnosis method of bridge spanning the sea
CN108846197B (en) * 2018-06-11 2022-05-20 石家庄铁道大学 Bridge girder erection machine girder damage identification and damage degree quantitative analysis method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104750926A (en) * 2015-03-27 2015-07-01 东南大学 Variable cross-section beam damage identification method based on node curvature and wavelet analysis
CN106897510A (en) * 2017-02-16 2017-06-27 西南交通大学 A kind of bridge structure 3-D seismics vulnerability analysis method
CN107085037A (en) * 2017-04-25 2017-08-22 湘潭大学 The vibration shape weights the girder construction damnification recognition method of Modal Flexibility
CN106896156B (en) * 2017-04-25 2019-06-14 湘潭大学 The girder construction damnification recognition method of uniform load face curvature difference by cross
CN109543303A (en) * 2018-11-22 2019-03-29 华北水利水电大学 A method of the Damage Assessment Method to be perturbed based on class curvature of the flexibility difference matrix and frequency

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
"Statistical Pattern Recognition for Railway Bridge Structural Damage Detection";Deshan Shan等;《2010 International Conference on Intelligent System Design and Engineering Application》;20101031;全文 *
"基于倾角影响线的简支梁桥损伤识别";张延庆等;《河北工业科技》;20170531;第34卷(第3期);正文第3.1节 *
"基于动力特性的梁式结构损伤识别研究";苏彬建;《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑（月刊）》;20190215(第02期);正文第3章 *

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