CN110487579B - Beam structure damage identification method based on inclination slope - Google Patents

Beam structure damage identification method based on inclination slope Download PDF

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CN110487579B
CN110487579B CN201910801892.8A CN201910801892A CN110487579B CN 110487579 B CN110487579 B CN 110487579B CN 201910801892 A CN201910801892 A CN 201910801892A CN 110487579 B CN110487579 B CN 110487579B
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damage
inclination angle
slope
measuring point
beam structure
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CN110487579A (en
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唐盛华
刘宇翔
张学兵
秦付倩
杨文轩
成鹏
张佳奇
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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
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Abstract

The invention discloses a beam structure damage identification method based on an inclination slope, which comprises the following steps: respectively applying the same load to the beam structures before and after damage to obtain actual measurement inclination angle curves of the beam structures before and after damage; calculating the slope of the dip angle curve before and after the beam structure is damaged, and carrying out damage positioning through the difference of the slope of the dip angle; carrying out quantitative analysis on the damage degree through the relative change of the inclination slope of the beam structure before and after damage; if the beam structure is a statically indeterminate structure, a group of orthogonal loads are adopted to act on the beam structure before and after damage respectively to obtain inclination angle slope differences under the action of a plurality of loads, and the inclination angle slope absolute value differences are summed to perform damage positioning and quantitative analysis. The method can accurately position and quantitatively analyze the damage of the beam structure, and is applied to the damage assessment of the beam structure.

Description

Beam structure damage identification method based on inclination slope
Technical Field
The invention belongs to the field of beam structure health monitoring, and particularly relates to a beam structure damage identification method based on an inclination slope.
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, and the structural damage identification method based on the static parameters can effectively avoid the uncertain influences of quality, particularly damping and the like. Meanwhile, the existing measuring equipment and technology are advanced and mature, and a quite accurate measured value of the structure can be obtained at a low cost, so that the structure damage identification technology based on the static parameters is widely researched.
The indexes of the structural damage identification technology based on static parameters, which are researched more, are indexes based on deflection, static strain, support reaction force influence line indexes and the like, but the structural damage identification calculation based on the parameters of the deflection, the static strain, the support reaction force and the like is complex.
Disclosure of Invention
In order to solve the technical problem of beam structure damage identification, the invention provides a beam structure damage identification method based on inclination slope.
The technical scheme for solving the technical problems comprises the following steps:
(1) respectively applying the same load to the beam structures before and after damage to obtain actual measurement inclination angle curves of the beam structures before and after damage;
(2) calculating the inclination angle slope before and after the beam structure is damaged, and carrying out damage positioning according to the inclination angle slope difference;
(3) carrying out quantitative analysis on the damage degree according to the relative change of the inclination slope of the beam structure before and after damage;
(4) if the beam structure is a statically indeterminate structure, a group of orthogonal loads are adopted to act on the beam structure before and after damage respectively to obtain inclination angle slope differences under the action of a plurality of loads, and the inclination angle slope absolute value differences are summed to perform damage positioning and quantitative analysis.
Specifically, in the step (2), the inclination slope θ' is calculated by the inclination of two adjacent measuring points:
Figure BDA0002182555210000021
wherein, theta is an inclination angle, subscript i is a measuring point number, and epsilon is a distance from a measuring point i-1 to a measuring point i.
Further, in the step (2), the differential tilt angle damage localization index DI is:
Figure BDA0002182555210000022
wherein, theta'iu、θ′idThe inclination slope of the ith measuring point structure under the load action before and after damage is respectively, n is the number of the measuring points, the measuring points No. 1 are arranged at one end of the beam structure, the measuring points No. n are arranged at the other end of the beam structure, the number of the measuring points is continuous and is increased from 1 to n, and i is more than or equal to 2 and less than or equal to n.
Specifically, in step (3), the structural damage degree is calculated as:
De＝[0 De2 … Dei … Den]；
wherein D iseiThe unit damage degree between a measuring point i-1 and a measuring point i identified by the ith measuring point;
the damage degree of the i measuring point is calculated as:
Figure BDA0002182555210000031
further, in the step (4), for the statically indeterminate structure, the distance between the zero points of the inclination slope curve under the action of each load is the largest by the obtained orthogonal load.
Selecting m orthogonal loads, wherein the absolute value difference of the inclination angle slopes of the structure before and after damage under the action of k loads is;
δθ′k＝|θ′dk|-|θ′uk|＝[0 |θ′2dk|-|θ′2uk|…|θ′idk|-|θ′iuk|…|θ′ndk|-|θ′nuk|]；
wherein, theta'uk、θ′dkIs the inclination angle slope before and after the structural damage under the k load respectively, theta'iuk、θ′idkThe inclination angle slopes before and after the structure is damaged under the k load action of the ith measuring point respectively, m is the number of orthogonal loads, m is more than or equal to 2, and k is more than or equal to 1 and less than or equal to m.
And (3) taking the absolute value difference of inclination angle slopes of m orthogonal loads for summing to carry out damage positioning:
Figure BDA0002182555210000032
the hyperstatic structural damage degree was calculated as:
Dea＝[0 Dea2 … Deai … Dean]；
wherein D iseaiThe unit damage degree between a measuring point i-1 and a measuring point i identified by the ith measuring point of the statically indeterminate beam structure is determined;
the method for calculating the damage degree of the measuring point i comprises the following steps:
Figure BDA0002182555210000033
furthermore, in the steps (1) and (4), the positions of the measuring points for the inclination angle test before and after the structure damage are arranged the same, and the number of the measuring points is not less than 6.
The invention has the technical effects that: the method applies the same load to the beam structure before damage and the beam structure after damage to obtain the difference between the tilt angles of each measuring point of the beam structure before damage and the tilt angle of the damage, carries out damage positioning according to the obtained difference between the tilt angles, establishes an explicit expression for calculating the damage degree according to the tilt angles of the beam structure before damage and the tilt angle of the damage, can directly calculate the damage degree according to the tilt angle, and provides the beam structure damage positioning and quantitative analysis method with low cost and high accuracy.
Drawings
FIG. 1 is a block flow diagram of the present invention.
FIG. 2 is a schematic diagram of a simple beam structure model according to the present invention.
FIG. 3 shows the action of unit bending moment of the simply supported beam of the present invention
Figure BDA0002182555210000041
Moment diagram of position.
FIG. 4 is a bending moment diagram of the unit bending moment of the measuring point of the basic structure i-1 of the simply supported beam.
FIG. 5 is a bending moment diagram of the unit bending moment of the i-point of the basic structure of the simply supported beam.
FIG. 6 is a moment diagram of the unit moment of the basic structure of the simply supported beam i + 1.
FIG. 7 is a view of the bending moment of the simply supported beam structure with uniform load distribution.
FIG. 8 is a slope curve diagram of the uniformly distributed load action inclination angle of the simply supported beam structure of the present invention.
FIG. 9 is a schematic view of the full-bridge uniform load effect of the three-span continuous beam.
FIG. 10 is a slope curve diagram of the inclination angle of the three-span continuous beam full-bridge uniform load action structure.
FIG. 11 is a schematic view of the first span uniform load of the three-span continuous beam of the present invention.
FIG. 12 is a schematic view of the second span uniform load of the three-span continuous beam of the present invention.
FIG. 13 is a schematic view of the third span uniform load of the three-span continuous beam of the present invention.
FIG. 14 is a slope curve diagram of the inclination angle of the three-span continuous beam span-by-span uniformly-distributed loading action structure.
FIG. 15 is a schematic finite element model diagram of a simply supported beam according to an embodiment of the present invention.
Fig. 16 is a simplified beam damage positioning index DI according to an embodiment of the present invention.
FIG. 17 is a diagram of a quantitative analysis index D of the damage degree of a simply supported beam in an embodiment of the present inventione。
FIG. 18 is a diagram of a finite element model of a second cantilever according to an embodiment of the present invention.
Fig. 19 shows a cantilever beam condition 1 damage localization index DI according to the second embodiment of the present invention.
Fig. 20 shows a cantilever beam condition 2 damage localization index DI in the second embodiment of the present invention.
FIG. 21 is a diagram showing a quantitative analysis index D of the damage degree of the cantilever beam under the working condition 1 in the second embodiment of the present inventione。
FIG. 22 is a diagram of a quantitative analysis index D of the damage degree of the cantilever beam under the working condition 2 in the second embodiment of the present inventione。
FIG. 23 is a finite element model diagram of a three-span continuous beam according to an embodiment of the present invention.
FIG. 24 shows a damage localization index DI where a load acts on a 6-point measurement in the third embodiment of the present invention.
FIG. 25 is a diagram showing a damage localization index DI where a load acts on a 19-point measurement in the third embodiment of the present invention.
FIG. 26 is a diagram showing a damage localization index DI where load acts on a 31-measuring point in the third embodiment of the present invention.
FIG. 27 shows the damage localization index DI under working condition 1 in the third embodiment of the present inventiona。
FIG. 28 is a quantitative analysis index D of the damage degree of the load acting on the 6 measuring points in the third embodiment of the present inventione。
FIG. 29 is a diagram showing a quantitative analysis index D of the damage degree of a load acting on a 19-measuring point in the third embodiment of the present inventione。
FIG. 30 is a diagram showing a quantitative analysis index D of the damage degree of a load acting on a 31 measurement point in the third embodiment of the present inventione。
FIG. 31 is a quantitative analysis index D of damage degree under condition 1 in the third embodiment of the present inventionea。
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The implementation flow of the invention is shown in fig. 1, and the specific steps are as follows:
step 1: respectively applying the same load to the beam structures before and after damage to obtain actual measurement inclination angle curves of the beam structures before and after damage;
step 2: calculating the inclination angle slope before and after the beam structure is damaged, and carrying out damage positioning according to the inclination angle slope difference;
and step 3: carrying out quantitative analysis on damage degree through relative change of inclination angle slopes before and after structural damage;
and 4, step 4: if the beam structure is a statically indeterminate structure, a group of orthogonal loads are adopted to respectively act on the structure before and after damage, so that the inclination angle slope difference under the action of a plurality of loads is obtained, and the inclination angle slope absolute value difference is summed for damage positioning and quantitative analysis.
In step 1, taking the uniform load distribution effect of the simply supported beam as an example, the structural model is shown in FIG. 2, the span is L, the distance between the damage position and the left end is a, the damage length is epsilon, the rigidity of the undamaged structure is EI, and the rigidity of the damage unit is EId. Unit bending moment M is 1 acting on left pivot
Figure BDA0002182555210000061
The bending moments in position are (as in fig. 3):
Figure BDA0002182555210000062
in the formula, x represents the distance from the beam left pivot point a.
The unit bending moment M is 1 and acts on the i-1 measuring point and the i and i +1 measuring points respectively, a bending moment graph acting on each measuring point is obtained as shown in figures 4-6, a bending moment graph M under the action of uniformly distributed loads q is shown in figure 7, and the expression of the bending moment at the x position is as follows:
Figure BDA0002182555210000063
when the structure is not damaged, any point under the action of uniformly distributed load is arranged
Figure BDA0002182555210000064
The inclination angle of the position is:
Figure BDA0002182555210000065
in the formula, the subscript "u" represents the state of intact structure.
When the structure is damaged, the inclination angles of the i-1 measuring point and the i +1 measuring point under the action of uniformly distributed load are respectively as follows:
Figure BDA0002182555210000066
Figure BDA0002182555210000067
Figure BDA0002182555210000068
in the formula, thetaidAnd (3) an external load action inclination angle after the structure of the point i is damaged is shown, and the subscript "d" shows the damage state of the structure.
In step 2, the inclination slope is calculated by adopting adjacent measuring points:
Figure BDA0002182555210000071
Figure BDA0002182555210000072
Figure BDA0002182555210000073
Figure BDA0002182555210000074
from the above derivation, θ'iu＝θ′idWhen the cell between the i, i +1 test points is not damaged, the EIdWhen being EI, θ'(i+1)u＝θ′(i+1)dThat is, theoretically, the difference between the pre-damage and post-damage inclination angles is 0 in the undamaged unit, and when the structure is damaged, θ'(i+1)u≠θ′(i+1)dTherefore, the damage location can be performed by the difference between the pre-damage and post-damage inclination angles, and the calculation method of the damage location index DI is as follows:
DI＝[DI1 DI2 … DIi … DIn-1 DIn] (11)
DIi＝θ′id-θ′iu (12)
in the formula: n is the number of measuring points, the slope of the measuring point 1 at the supporting position of the side of the beam structure can not be calculated, and DI is taken1＝0。
In step 3, the following equations (9) and (10) show that:
Figure BDA0002182555210000075
therefore, the damage degree of the cell between the i and i +1 measuring points can be obtained as follows:
Figure BDA0002182555210000076
the inclination slope of the simply supported beam under the action of uniformly distributed load is shown in fig. 8, and it can be seen that, except for the side supporting points, no point with inclination slope of 0 exists in the middle measuring point, i.e. the denominator in the formula (14) is not 0, so that the damage of each part of the simply supported beam can be quantitatively analyzed.
In step 4, for a statically indeterminate structure, taking a three-span continuous beam as an example, when a full-bridge uniformly-distributed load is adopted for loading, a zero point exists on an inclination slope curve, so that the damage degree cannot be accurately identified at the zero point by the damage quantitative analysis formula of the formula (14), and sudden change can occur.
As shown in fig. 9 and 10, when the uniform load is fully distributed, 4 zero point damages of inclination angle and slope can not be identified. Therefore, orthogonal loads are considered, for example, a step-by-step loading mode is adopted for a three-span continuous beam, as shown in fig. 11 to 14, at this time, only two inclination slope zero points are provided under each load condition, the zero point positions under the action of each load are different, and the problem that damage at the inclination slope zero points cannot be identified by performing absolute value superposition on the DI index subjected to step-by-step loading is considered. For other types of statically indeterminate structures, the orthogonal loads are preferably selected to maximize the distance between the zero point of the declination slope under each load.
Selecting m orthogonal loads, wherein the absolute value difference of the inclination angle slopes of the structure before and after damage under the action of k loads is;
δθ′k＝|θ′dk|-|θ′uk|＝[0 |θ′2dk|-|θ′2uk|…|θ′idk|-|θ′iuk|…|θ′ndk|-|θ′nuk|] (15)
wherein, theta'uk、θ′dkIs the inclination angle slope before and after the structural damage under the k load respectively, theta'iuk、θ′idkThe inclination angle slopes before and after the structure is damaged under the k load action of the ith measuring point respectively, m is the number of orthogonal loads, m is more than or equal to 2, and k is more than or equal to 1 and less than or equal to m.
And (3) taking the absolute value difference of inclination slope curves of m orthogonal loads for summation to carry out damage positioning:
Figure BDA0002182555210000081
the calculation method of the hyperstatic structure damage degree comprises the following steps:
Dea＝[0 Dea2 … Deai … Dean] (17)
wherein D iseaiAnd identifying the structural damage degree of the ith measuring point of the statically indeterminate beam structure.
The damage degree calculation method comprises the following steps:
Figure BDA0002182555210000091
in the steps 1 and 4, the positions of the measuring points of the inclination angle test before and after the structure is damaged are arranged the same, and the number of the measuring points is not less than 6.
The first embodiment is as follows: referring to fig. 15, 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 BDA0002182555210000092
The specific implementation steps are as follows:
step 1: and respectively applying uniform loads of 120N/m to the simply supported beam before and after the damage to obtain the actually measured inclination angle curve of the simply supported beam before and after the damage.
Step 2: the slope of the dip angle before and after the structural damage is calculated, and the damage is positioned through the difference of the slope angles of the dip angles, as shown in fig. 16, the result shows that obvious peak values appear at the positions of the units 1 and 10, DI at the positions of other undamaged positions is 0, and the index can identify all the damages.
And step 3: quantitative analysis of damage degree is carried out through relative change of inclination angle slope before and after structural damage, and damage degree index D of multi-damage working condition 1-2eThe identification effect is as shown in fig. 17, the index can accurately carry out quantitative analysis on the damage degree, the identified damage degree is very close to the actual damage degree, and the index can accurately identify the damage degree of the simply supported beam.
Example two: referring to fig. 18, 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 BDA0002182555210000101
The specific implementation steps are as follows:
step 1: and respectively applying 10N concentrated loads to the cantilever ends of the cantilever beams before and after the damage to obtain actual measurement inclination angle curves before and after the damage of the cantilever beams.
Step 2: the slope of the dip angle before and after the structural damage is calculated, the damage is positioned through the dip angle slope difference, the damage positioning index DI identification result of the working condition 1 is shown in figure 19, the unit 1, the unit 10 and the unit 20 have peak values with unequal degrees, the index can accurately identify the damage positions of multiple damages without interfering the peak values, the damage positioning index DI identification result of the working condition 2 is shown in figure 20, the unit 1 and the unit 10 have obvious peak value bulges, which shows that the unit 1 and the unit 10 are damaged, the bulge of the free end unit 20 is smaller, and the damage can be further judged through the damage degree index.
And step 3: quantitative analysis of damage degree is carried out through relative change of inclination angle slope before and after structural damage, and damage quantitative analysis indexes D of working condition 1 and working condition 2eThe recognition effects are as shown in fig. 21 and 22, respectively, and not only can it be determined 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. 23, 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.
TABLE 3 Damage Condition of three-span continuous Beam
Figure BDA0002182555210000111
The specific implementation steps are as follows:
step 1: the continuous beam is of a statically indeterminate structure, so a group of orthogonal loads are taken, concentrated loads 120N are respectively applied to the measuring point 6 (first span middle), the measuring point 19 (middle span middle) and the measuring point 31 (third span middle), and actual measurement inclination angle curves before and after damage of the continuous beam under the action of each load are obtained.
Step 2: calculating the slope of the dip angle before and after the structural damage, and carrying out damage positioning by summing the absolute value difference of the slope of the dip angle, wherein the damage positioning index DI identification results under the independent action of each load under the working condition 1 are shown in figures 24-26, thus all the three damages can be identified, and after the superposition, the damage positioning indexes can be used for overlappingIndex DI ofaSee FIG. 27, 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: quantitative analysis of damage degree is carried out through the absolute value and relative change of inclination slope before and after structural damage, and the damage degree quantitative analysis index D under the independent action of each load under the working condition 1eThe identification results are shown in fig. 28-30, all of which have abnormal peak interference and influence the identification of damage degree, and as shown in fig. 30, the easily-distinguished units 26 and 27 have damage, only the unit 26 is actually damaged, and the superposed index DeaThe recognition result is shown in fig. 31, only a larger value is found at the damage position, the recognition result is close to the actual damage degree, and the influence of the inclination slope zero point on the damage recognition can be effectively avoided by adopting the orthogonal load superposition index for the hyperstatic structure.
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 (2)

1. A beam structure damage identification method based on inclination slope is characterized by comprising the following steps:
(1) respectively applying the same load to the beam structures before and after damage to obtain actual measurement inclination angle curves of the beam structures before and after damage;
(2) calculating the inclination angle slope before and after the beam structure is damaged, and carrying out damage positioning according to the inclination angle slope difference, wherein the inclination angle slope theta' is calculated through the inclination angles of two adjacent measuring points as follows:
Figure FDA0002963805550000011
wherein theta is an inclination angle, subscript i is a measuring point number, and epsilon is a distance from a measuring point i-1 to a measuring point i;
the differential dip angle damage index DI is:
DI＝[DI1 DI2 … DIi … DIn]
＝[0 θ′2d-θ′2u … θ′id-θ′iu … θ′nd-θ′nu]；
wherein, theta'iu、θ′idThe slope of the inclination angle under the load action before and after the structure of the ith measuring point is damaged respectively, n is the number of the measuring points, the measuring point No. 1 is arranged at one end of the beam structure, the number of the measuring points No. n is continuous and increases from 1 to n in sequence, i is more than or equal to 2 and less than or equal to n, and DIi is the slope difference damage positioning index of the inclination angle curve at the ith measuring point;
(3) carrying out quantitative analysis on the damage degree according to the relative change of the inclination angle slope before and after the damage of the beam structure, wherein the calculation of the damage degree of the structure is as follows:
De＝[0 De2 … Dei … Den]；
wherein D iseiThe unit damage degree between a measuring point i-1 and a measuring point i identified by the ith measuring point;
the damage degree of the i measuring point is calculated as:
Figure FDA0002963805550000012
(4) if the beam structure is a statically indeterminate structure, a group of orthogonal loads are adopted to respectively act on the beam structure before and after damage to obtain inclination angle slope differences under the action of a plurality of loads, and the absolute value differences of the inclination angle slopes are summed to carry out damage positioning and quantitative analysis;
selecting m orthogonal loads, wherein the absolute value difference of the inclination angle slopes of the structure before and after damage under the action of k loads is;
δθ′k＝|θ′dk|-|θ′uk|＝[0 |θ′2dk|-|θ′2uk| … |θ′idk|-|θ′iuk| … |θ′ndk|-|θ′nuk|]；
wherein, theta'uk、θ′dkIs the inclination angle slope before and after the structural damage under the k load respectively, theta'iuk、θ′idkInclination slopes before and after structural damage under the k load action of the ith measuring point are respectively shown, m is the number of orthogonal loads, m is more than or equal to 2, k is more than or equal to 1 and less than or equal to m;
and (3) taking the absolute value difference of inclination angle slopes of m orthogonal loads for summing to carry out damage positioning:
Figure FDA0002963805550000021
the hyperstatic structural damage degree was calculated as:
Dea＝[0 Dea2 … Deai … Dean]；
wherein D iseaiThe unit damage degree between a measuring point i-1 and a measuring point i identified by the ith measuring point of the statically indeterminate beam structure is determined;
the damage degree of the i measuring point is calculated as:
Figure FDA0002963805550000022
2. the tilt slope based beam structure damage identification method of claim 1, wherein: in the steps (1) and (4), the positions of the measuring points for the inclination angle test before and after the structure is damaged are arranged the same, and the number of the measuring points is not less than 6.
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