CN110472369B - Beam structure damage identification method for deflection curvature - Google Patents

Abstract

The invention discloses a beam structure damage identification method of deflection curvature. The steps are as follows: respectively apply the same load to the beam structure before and after the damage, and obtain the measured deflection curve of the beam structure before and after the damage; calculate the curvature of the deflection before and after the structure damage, by The difference in deflection and curvature is used to locate the damage; the degree of damage is quantified by the relative change of the deflection and curvature before and after the structure is damaged; if the beam structure is a statically indeterminate structure, a group of orthogonal loads are applied to the structure before and after the damage respectively to obtain multiple load effects The difference in deflection and curvature is calculated by taking the sum of the absolute value difference of deflection and curvature to locate and quantify the damage. The invention can accurately locate and quantify the damage of the beam structure, and is applied to the damage assessment of the beam structure.

Description

Damage Identification Method of Beam Structure Based on Deflection Curvature

Technical Field

The invention belongs to the technical field of structural health monitoring, and in particular relates to a beam structure damage identification method based on deflection curvature in beam structure nondestructive testing technology.

Background Art

Structural damage identification is the core content of the bridge health monitoring system, and there are many identification methods. The overall damage identification methods developed at home and abroad mainly include: structural damage identification methods based on dynamic response and static response. The dynamic response parameter index mainly judges structural damage through the change of structural mode (vibration frequency and vibration mode). This method has high requirements on the number of measuring points, sensor measurement accuracy, modal parameter identification method, etc. Another method is the damage identification method based on static response parameters. The static response test technology is simple and mature, and the test data is highly accurate. It can effectively avoid the uncertainty of mass, especially damping. Damage identification indicators based on static response parameters mainly include static deflection indicators, static strain indicators, and support reaction influence line indicators.

The static deflection index is mainly divided into the static deflection method, the deflection influence line method and the static deflection curvature method. Cui Fei et al. used the moment of inertia of the structural unit as the parameter to be identified, established the sensitivity matrix of the parameter to be identified to the structural deflection, strain and other parameters, and obtained the structural parameter change information to determine the damage location. Liu Gang et al. used the difference in deflection before and after damage of the statically determinate structure to be similar to the shape of the influence line generated by the concentrated force acting on the damaged unit, and identified the structural damage through the damage force influence line. Chen Jihao et al. used the different deflection difference curves when the load was located in the intact and damaged areas to identify damage, and analyzed the identification effect of the index through a hollow plate example. Du Yongfeng et al. derived the functional relationship between the deflection difference influence line and the position of the moving load, pointed out that there was a difference in the functional relationship when the moving load was located in the damaged area and the intact area, and then identified the damage location. Zhu S Y et al. fitted the deflection influence line of the structure, analyzed the fitted influence line, and established the damage identification index using the influence line data before and after the structural damage. Yam et al. conducted sensitivity analysis on the damage factors of the deflection, deflection slope and deflection curvature of plate structures through finite element models to identify structural damage. Wang Yilin combined the curvature with the static deflection of the structure, used the adjacent difference method to obtain the differential curvature under static load, and used the adjacent differential curvature difference index to identify the damage of single-span beams. Abdo studied the relationship between damage characteristics and changes in deflection curvature, and used the change in deflection curvature as a damage index for structural damage identification. Yang Xiao et al. respectively gave formulas for calculating curvature using the deflection and strain of beam structures, used the relative curvature difference before and after beam damage to identify the damage location, and proposed a two-stage damage identification method for statically determinate beams based on static bending.

Although much research has been done on structural damage location methods based on deflection indicators, there are not many methods related to the quantitative determination of damage extent, and it is rare to see methods that directly use static deflection curvature to quantify the degree of structural damage.

Summary of the invention

Aiming at the shortcoming that the existing deflection curvature method cannot identify the degree of structural damage, the present invention provides a beam structure damage identification method based on deflection curvature.

The above object of the present invention is achieved through the following technical solutions:

The beam structure damage identification method based on deflection curvature comprises the following steps:

(1) Apply the same load to the beam structure before and after damage to obtain the measured deflection curves of the beam structure before and after damage;

(2)(a) If the beam structure is statically determinate, the deflection curvature of the beam structure before and after damage is calculated, and the damage is located by the deflection curvature difference; the degree of damage is quantified by the relative change of the deflection curvature before and after damage.

(b) If the beam structure is an over-determined beam structure, a set of orthogonal loads are applied to the beam structure before and after damage according to step (1), and the deflection curvature of the deflection curve of the beam structure before and after damage is calculated to obtain the deflection curvature difference under multiple loads, and the damage is located by summing the absolute value difference of the deflection curvature; the degree of damage is quantified by the absolute value and relative change of the deflection curvature of the beam structure before and after damage;

In step (2), the deflection curvature w″ is calculated by central difference, and the calculation formula is as follows:

Where w is the deflection, subscript i is the measuring point number, and ε is the average value of the distance from measuring point i-1 to measuring point i and the distance from measuring point i to measuring point i+1;

In step (2)(a), if the beam structure is a statically determinate beam structure, the deflection curvature difference damage location index is as follows:

DI＝[DI ₁ DI ₂ ... DI _i ... DI _n-1 DI _n ]

=[0 w″ _2d -w″ _2u … w″ _id -w″ _iu … w″ _(n-1)d -w″ _(n-1)u 0];

Wherein, DI represents the damage location index of the statically determinate beam structure, DI _i represents the damage location index identified by the i-th measuring point of the statically determinate beam structure, w″ _iu and w″ _id are the deflection curvatures of the beam structure under load before and after damage at the i-th measuring point, respectively, and n is the number of measuring points. The measuring point No. 1 is arranged at one end of the beam structure, and the measuring point No. n is arranged at the other end of the beam structure. The number of measuring points is continuous and increases from 1 to n. i is greater than or equal to 2 and less than or equal to n-1.

In step (2)(a), the quantitative calculation method of the damage degree of the beam structure is as follows:

D _e = [0 D _e2 … D _ei … D _{e (n-1)} 0];

Where, _De is the quantitative index of the damage degree of the statically determinate beam structure, and _Dei is the damage degree identified at the i-th measuring point of the statically determinate beam structure;

For the middle unit of the beam structure, the damage degree calculation formula is as follows:

For the edge element of the beam structure, if the rotation angle is constrained, the damage degree calculation formula is as follows:

For the edge element of the beam structure, if the rotation angle is unconstrained, the damage degree calculation formula is as follows:

In step (2)(b), if the beam structure is an over-determined beam structure, the specific process of damage location and quantification is as follows:

For statically indeterminate beam structures, the orthogonal loads are selected so that the distance between the zero points of bending moment under each load is the largest;

Select m orthogonal loads, m is greater than or equal to 2, and the absolute value difference of the deflection curvature of the beam structure before and after damage under the k load δw″ _k is shown as follows;

δw″ _k ＝|w″ _dk |-|w″ _uk |＝[0 |w″ _2dk |-|w″ _2uk | … |w″ _idk |-|w″ _iuk | … |w″ _{(n-1) dk} |-|w″ _(n-1)uk |0];

Wherein, w″ _uk and w″ _dk are the deflection curvatures of the indeterminate beam structure before and after damage under load k, w″ _iuk and w″ _idk are the deflection curvatures of the indeterminate beam structure before and after damage under load k at the i-th measuring point, respectively, and k is greater than or equal to 1 and less than or equal to m;

The damage location is performed by taking the sum of the absolute value differences of the deflection curvature of m orthogonal loads. The calculation formula is as follows:

Where DI _a represents the damage localization index of the statically indeterminate beam structure;

The quantitative calculation method of the damage degree of the statically indeterminate beam structure is as follows:

D _ea = [0 D _ea2 … D _eai … D _{ea (n-1)} 0];

Where, _Dea represents the quantitative index of the damage degree of the statically indeterminate beam structure, and _Deai is the damage degree identified at the i-th measuring point of the statically indeterminate beam structure;

For the middle unit of the beam structure, the damage degree calculation formula is as follows:

For the edge element of the beam structure, if the rotation angle is constrained, the damage degree calculation formula is as follows:

For the edge element of the beam structure, if the rotation angle is unconstrained, the damage degree calculation formula is as follows:

Specifically, in step (1), the measuring points for the deflection test of the beam structure before and after damage are arranged in the same position, and the number of measuring points is not less than 6.

The present invention applies the same load to the beam structure before and after damage, obtains the difference in deflection curvature before and after damage at each measuring point of the beam structure, and locates the damage. At the same time, an explicit expression for calculating the degree of damage from the deflection curvature before and after damage is established, and the degree of damage can be directly calculated from the deflection curvature. Through the calculation examples of simply supported beams, cantilever beams and three-span continuous beams, considering a variety of damage conditions, the application value of the deflection curvature index in beam structure damage identification is verified, and an effective new method is provided for beam structure damage location and quantification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is a diagram of a single-span beam structure model of the present invention.

FIG3 is a bending moment diagram of a unit force acting on the i-1 measuring point of the basic structure of a simply supported beam of the present invention.

FIG. 4 is a bending moment diagram of a unit force acting at measuring point i of the basic structure of a simply supported beam of the present invention.

FIG. 5 is a bending moment diagram of a unit force acting at the i+1 measuring point of the basic structure of a simply supported beam of the present invention.

FIG. 6 is a bending moment diagram of the single-span beam structure under external load of the present invention.

FIG. 7 is a schematic diagram of uniformly distributed load on the entire three-span continuous beam bridge of the present invention.

FIG8 is a structural deflection diagram of the three-span continuous beam full bridge under uniformly distributed load of the present invention.

FIG. 9 is a schematic diagram of uniformly distributed load on the first span of the three-span continuous beam of the present invention.

FIG. 10 is a schematic diagram of uniformly distributed load on the second span of the three-span continuous beam of the present invention.

FIG. 11 is a schematic diagram of uniformly distributed load on the third span of the three-span continuous beam of the present invention.

FIG. 12 is a diagram showing the structural deflection of a three-span continuous beam of the present invention under uniformly distributed loads on each span.

FIG. 13 is a finite element model diagram of a simply supported beam according to an embodiment of the present invention.

FIG. 14 is a curve diagram of the damage location index DI of a simply supported beam in the first embodiment of the present invention.

FIG. 15 is a curve diagram of the quantitative indicator _De of the degree of damage of a simply supported beam in the first embodiment of the present invention.

FIG. 16 is a finite element model diagram of a cantilever beam according to a second embodiment of the present invention.

FIG. 17 is a damage location index DI curve diagram of the cantilever beam working condition 1 in the second embodiment of the present invention.

FIG. 18 is a damage location index DI curve diagram of the cantilever beam working condition 2 in the second embodiment of the present invention.

FIG. 19 is a curve diagram of the quantitative indicator _De of the damage degree of the cantilever beam in working condition 1 in the second embodiment of the present invention.

FIG. 20 is a curve diagram of the quantitative indicator _De of the damage degree of the cantilever beam in working condition 2 in the second embodiment of the present invention.

Figure 21 is a finite element model diagram of a three-span continuous beam according to embodiment 3 of the present invention.

FIG. 22 is a curve diagram of the damage location index DI _a of working condition 1 in the third embodiment of the present invention.

FIG. 23 is a damage location index DI curve diagram of working condition 1 in embodiment 3 of the present invention.

FIG. 24 is a curve diagram of the damage location index DI _a of working condition 2 in the third embodiment of the present invention.

FIG. 25 is a damage location index DI curve diagram of working condition 2 in embodiment 3 of the present invention.

FIG. 26 is a curve diagram of the damage location index DI _a of working condition 3 in the third embodiment of the present invention.

FIG. 27 is a curve diagram of the quantitative indicator _Dea of the degree of damage in working condition 1 in the third embodiment of the present invention.

FIG. 28 is a curve diagram of the quantitative indicator _De of the degree of damage in working condition 1 in the third embodiment of the present invention.

FIG. 29 is a curve diagram of the quantitative indicator _Dea of the degree of damage in working condition 2 in the third embodiment of the present invention.

FIG30 is a curve diagram of the quantitative indicator _De of the degree of damage in working condition 2 in the third embodiment of the present invention.

FIG31 is a curve diagram of the quantitative indicator _Dea of the degree of damage in working condition 3 in embodiment 3 of the present invention.

DETAILED DESCRIPTION

The present invention is further described below in conjunction with the accompanying drawings and embodiments. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements.

The beam structure damage identification method based on deflection curvature of the present invention is implemented as shown in the flowchart of FIG1 , and the specific steps are as follows:

Step 1: Apply the same load to the beam structure before and after damage to obtain the measured deflection curve of the beam structure before and after damage;

Step 2 (a): If the beam structure is a statically determinate beam structure, calculate the deflection curvature of the deflection curve of the beam structure before and after damage, and locate the damage by the deflection curvature difference; quantify the damage degree by the relative change of the deflection curvature before and after damage of the beam structure;

Step 2(b): If the beam structure is an over-determined beam structure, a set of orthogonal loads are applied to the beam structure before and after damage according to step 1. The deflection curvature of the deflection curve of the beam structure before and after damage is calculated to obtain the deflection curvature difference under multiple loads. The damage is located by summing up the absolute value difference of the deflection curvature. The degree of damage is quantified by the absolute value and relative change of the deflection curvature before and after damage.

Apply step 1, take a single-span beam as an example, its model diagram is shown in Figure 2, the span is L, A and B are the two ends of the single-span beam, the damage position is a from the left end, the damage length is ε, the stiffness of the undamaged beam structure is EI, and the stiffness of the damaged unit is EI _d . The unit force P = 1 acts on the i-1 measuring point and the i and i+1 measuring points respectively, and the bending moment diagrams acting on each measuring point are shown in Figures 3 to 5, and the bending moment diagram under the action of any external load q (x) is shown in Figure 6.

The bending moments under unit force are:

分别为图3～图5中的

x表示距梁结构左端点A的距离。In formula (1), j represents the sequence number. When j is 1, 2, or 3,

They are respectively in Figures 3 to 5

x represents the distance from the left end point A of the beam structure.

The deflection increments of each measuring point before and after damage are:

In the formula, _dwi represents the difference in deflection of the beam structure under external load before and after damage at the i-th measuring point, w _iu and w _id represent the deflection of the beam structure under external load before and after damage at the i-th measuring point, respectively, and the subscripts "u" and "d" represent the undamaged state and damaged state of the beam structure, respectively.

Applying step 2(a), the deflection curvature after damage at measuring point i is calculated using the central difference method:

Wherein, w″ _iu and w″ _id represent the deflection curvature of the beam structure at the i-th measuring point under load before and after damage, respectively, and dw″ _i represents the difference in deflection curvature of the beam structure at the i-th measuring point under load before and after damage.

Assuming that the bending moment of the damaged unit under the external load changes approximately in a linear relationship, let the bending moment under the external load at the i-th measuring point be _Mi , then the bending moment between the damaged units is:

M＝M _i +K(xa) (7);

Where K is the slope of the bending moment change. Substituting equation (7) into equation (6), we get:

When the unit between measuring points i and i+1 is undamaged, that is, EI _d = EI, dw″ _i = w″ _id - w″ _iu = 0, that is, theoretically, the deflection curvature difference before and after damage is 0 at the undamaged unit. When the beam structure is damaged, dw″ _i ≠ 0, so the damage can be located by the deflection curvature difference before and after damage. The calculation method of the damage location index DI is as follows:

DI＝[DI ₁ DI ₂ ... DI _i ... DI _n-1 DI _n ] (9);

DI _i =w″ _id -w″ _iu (10);

In formula (9), DI represents the damage localization index of the statically determinate beam structure, DI _i represents the damage localization index identified at the i-th measuring point of the statically determinate beam structure, and n is the number of measuring points. The curvature of the measuring points at the side supports of the beam structure cannot be calculated, so DI ₁ = DI _n = 0.

Apply step 2(a). For the opposite edge element, if it is a degree of freedom, such as a simply supported end or a cantilever end, the bending moment at the support is 0, that is:

M _i +Kε＝0 (11);

Substituting formula (11) into formula (8) yields:

From material mechanics, we know that there is the following relationship between structural stiffness, bending moment and deflection curvature:

Where: ρ represents the radius of curvature, and w″ represents the curvature of the beam structure deflection.

The theoretical deflection curvature of the i measuring point when the beam structure is not damaged is:

In formula (14), w″ _iut represents the theoretical deflection curvature of the i measuring point when the beam structure is not damaged.

Then the theoretical deflection curvature of the i measuring point when the beam structure is damaged is:

In formula (15), w″ _idt represents the theoretical deflection curvature of measuring point i when the beam structure is damaged.

Therefore, the curvature of the i measuring point can be obtained as:

The damage degree of the beam structure can be obtained as:

For the intermediate unit and the edge supports with constrained rotation, such as the fixed end, assuming that the bending moment increment is very small, that is, 3M _i >> Kε, then equation (8) is simplified to:

The theoretical damage degree can be obtained as:

Applying step 2(b), for an over-determined structure, taking a three-span continuous beam as an example, when a uniformly distributed load is applied, there will be an inflection point in the deflection curve, that is, there is a point where w″=0, so the corresponding bending moment is also 0. At this time, regardless of the value of EI, equation (13) is always valid. Therefore, the indicator cannot identify the damage occurring at the inflection point.

Refer to Figures 7 and 8. When the uniformly distributed load is fully distributed, there are 4 inflection points (hereinafter referred to as inflection points) where damage cannot be identified. Therefore, consider using span-by-span loading for the three-span continuous beam, as shown in Figures 9 to 12. At this time, there are only two inflection points under each load condition, and the inflection point positions under each load are different. Consider superimposing the absolute values of the DI index after span-by-span loading to avoid the problem of being unable to identify damage at the inflection points. For other types of statically indeterminate structures, the orthogonal loads should be taken to maximize the distance between the zero points of the bending moment under each load.

Select m orthogonal loads, m is greater than or equal to 2, and the absolute value difference of the deflection curvature before and after the structure is damaged under the action of load _k is:

δw″ _k ＝|w″ _dk |-|w″ _uk |＝[0 |w″ _2dk |-|w″ _2uk | … |w″ _idk |-|w″ _iuk | … |w″ _{(n-1) dk} |-|w″ _(n-1)uk | 0] (23);

Among them, w″ _uk and w″ _dk are the deflection curvatures of the statically indeterminate beam structure before and after damage under the action of load k, w″ _iuk and w″ _idk are the deflection curvatures of the statically indeterminate beam structure before and after damage under the action of load k at the i-th measuring point, and k is greater than or equal to 1 and less than or equal to m.

The damage location is performed by summing the absolute value differences of the deflection curvature of m orthogonal loads:

Where DI _a represents the damage localization index of the statically indeterminate beam structure;

The calculation method of the damage degree of statically indeterminate structure is:

D _ea = [0 D _ea2 … D _eai … D _{ea (n-1)} 0] (25);

Where, _Dea represents the quantitative index of the damage degree of the statically indeterminate beam structure, and _Deai is the damage degree identified at the i-th measuring point of the statically indeterminate beam structure.

For the intermediate unit of the structure, the damage degree is calculated as follows:

In formula (26), w″ _iuk and w″ _idk are the deflection curvatures of the indeterminate beam structure before and after damage under the load at the i-th measuring point k, respectively.

For the edge element of the beam structure, if the rotation is constrained, such as the fixed end, the damage degree is:

For the edge element of the beam structure, if the rotation angle is unconstrained, such as the simply supported end or cantilever end, the damage degree is:

In step 1, the measuring points for the deflection test of the beam structure before and after damage are arranged in the same position, and the number of measuring points is not less than 6.

Example 1: Referring to FIG13 , the span of the simply supported beam is 100 cm, 5 cm is divided into one unit, a total of 20 units, 21 measuring points (the numbers in the upper circle in the figure are unit numbers, and the numbers in the lower circle are measuring point numbers). The cross-sectional dimensions of the plate are b×h=4.5 cm×1.5 cm, the elastic modulus of the material is 2.7×10 ³ MPa, the Poisson's ratio is 0.37, and the density is 1200 kg/m ³ .

Damage in actual engineering structures, such as the generation of cracks, material corrosion or reduction of elastic modulus, generally only causes a large change in the stiffness of the structure, but has little effect on the quality of the structure. Therefore, in the finite element calculation, it is assumed that the damage of the structural unit only causes a decrease in the stiffness of the unit, but does not cause a change in the quality of the unit. The damage of the unit is simulated by the reduction of the elastic modulus. The beam structure model is established using the beam3 beam unit of ANSYS software. Taking the multi-unit damage condition as an example, considering that the edge unit 1 and the mid-span unit 10 are damaged to different degrees at the same time, the damage condition is shown in Table 1.

Table 1 Multiple damage conditions of simply supported beams

The specific implementation steps are as follows:

Step 1: Apply a uniformly distributed load of 120 N/m to the simply supported beam before and after damage to obtain the measured deflection curve of the simply supported beam before and after damage.

Step 2 (damage location): Calculate the curvature of the deflection before and after structural damage, and locate the damage by the deflection curvature difference, as shown in Figure 14. The results show that obvious peaks appear at units 1 and 10, and the DI at other undamaged locations is 0. This indicator can identify all damage.

Step 2 (damage quantification): The damage degree is quantified by the relative change of the deflection curvature before and after the structural damage. The damage degree index _De identification effect of multiple damage conditions 1 to 2 is shown in Figure 15. This index can accurately quantify the damage degree. The theoretical damage degree is very close to the actual damage degree. The index can accurately identify the damage degree of the simply supported beam.

Example 2: Referring to FIG16 , the span of the cantilever beam is 100 cm, 5 cm is divided into one unit, a total of 20 units, 21 measuring points (the numbers in the upper circle in the figure are unit numbers, and the numbers in the lower circle are measuring point numbers). The plate cross-sectional dimensions are b×h=4.5 cm×1.5 cm, the material elastic modulus is 2.7×10 ³ MPa, the Poisson's ratio is 0.37, and the density is 1200 kg/m ³ .

Considering that the fixed-end unit 1, the mid-span unit 10, and the free-end unit 20 all suffer damage to varying degrees, the damage conditions are shown in Table 2.

Table 2 Multiple damage conditions of cantilever beam

The specific implementation steps are as follows:

Step 1: Apply a concentrated load of 120N to the cantilever end of the cantilever beam before and after damage to obtain the measured deflection curve of the cantilever beam before and after damage.

Step 2 (damage location): Calculate the curvature of the deflection before and after the structural damage, and locate the damage by the deflection curvature difference. The damage location index DI identification result of working condition 1 is shown in Figure 17. Unit 1, unit 10, and unit 20 have peaks of varying degrees. This indicator can accurately identify the damage locations of multiple damages without interfering peaks. The damage location index DI identification result of working condition 2 is shown in Figure 18. Unit 1 and unit 10 have obvious peak bulges, indicating that unit 1 and unit 10 are damaged. The bulge of free end unit 20 is smaller, but it can also show that it is damaged.

Step 2 (damage quantification): The damage degree is quantified by the relative change of the deflection curvature before and after the structural damage. The _{identification} effects of the damage quantification index De for working condition 1 and working condition 2 are shown in Figures 19 and 20, respectively. The identified damage degree is close to the actual damage.

Example 3: Referring to Figure 21, the span of the three-span continuous beam is arranged as 100+150+100cm, 10cm is divided into one unit, a total of 35 units, 36 measuring points (the numbers in the upper circle in the figure are unit numbers, and the numbers in the lower circle are support numbers). The plate cross-sectional dimensions are b×h=4.5cm×1.5cm, the material elastic modulus is 2.7×10 ³ MPa, the Poisson's ratio is 0.37, and the density is 1200kg/m ³ .

Unit 7 is located near the 0 point of the side span bending moment under the uniformly distributed load (i.e., the inflection point of the deflection curvature), unit 18 is the mid-span unit of the middle span, and unit 26 is the maximum negative moment unit of the third span. The damage conditions are shown in Table 3.

Table 3 Damage conditions of three-span continuous beams

The specific implementation steps are as follows:

Step 1: The continuous beam is an over-determined structure, so a set of orthogonal uniformly distributed loads is taken, and the uniformly distributed load is adopted for each span, as shown in Figures 9 to 11. That is, a uniformly distributed load of 120N/m is applied to each span, and the measured deflection curves of the continuous beam before and after damage under each load are obtained.

Step 2 (damage location): Calculate the curvature of the deflection before and after the structural damage, and locate the damage by summing the absolute value difference of the deflection curvature. The identification result of the damage location index DI _a for condition 1 is shown in Figure 22. An obvious peak occurs at unit 7. If the uniform load of the entire bridge is directly used, the identification result of the damage location index DI a for condition 1 is shown in Figure 23. It can be seen that the damage location can also be identified, but the peak of the damage location is not as obvious as the DI _a indicator. The identification result of the damage location index DI _a for condition 2 is shown in Figure 24. The damage location index DI _a of unit 7 at the inflection point has an obvious peak, which avoids the problem of the inflection point damage not being identified. The damage at the inflection point can also be well identified after the absolute value of the uniform load action index is superimposed on each span. If the uniform load of the entire bridge is directly used, the identification result of the damage location index DI a for condition 2 is shown in Figure 25. It can be seen that no obvious peak occurs in unit 7, indicating that the DI indicator when the uniform load is fully distributed cannot identify the damage of the unit near the inflection point. The identification result of the damage location index DI _a for condition 3 is shown in Figure 26. All three damages are identified, and the positioning effect is good. It can be seen that new inflection points are generated under the action of uniformly distributed loads on each span, but the positions of the inflection points generated by each uniformly distributed load are different. The influence of the inflection points can be avoided by superimposing the indicators.

Step 2 (damage quantification): The damage degree is quantified by the absolute value and relative change of the deflection curvature before and after structural damage. The damage quantification index _{Dea of} working condition 1 is shown in Figure 27. The identified theoretical damage degree is slightly smaller than the actual damage degree, with an error of -0.01. A peak appears near unit 14 at the undamaged position, which does not affect the identification result. The identification result of the damage quantification index _De of working condition 1 is shown in Figure 28. A peak appears near unit 7, but the damage degree cannot be accurately identified.

The quantitative indicator _{Dea of} damage degree for working condition 2 is shown in Figure 29. The damage degree recognition effect at the three locations is good, and the damage degree is basically the same as the actual value. There are small protrusions at measuring point 11 and measuring points 14 and 25, but the overall judgment effect of the damage degree is not affected by the combination of the damage position recognition result. The damage degree _De indicator is shown in Figure 30. There are many interference peaks, so the _De indicator cannot effectively identify the damage degree of the unit at the inflection point.

The identification effect of the quantitative indicator _Dea of damage degree in working condition 3 is shown in Figure 31. The damage degree identification results of units 7 and 18 are close to the actual damage degree. There is a bulge at measuring point 25, but it is a negative value. This is because measuring point 25 is at a new inflection point. Combined with the damage position identification, the influence of the damage degree interference peak on the identification effect can be accurately eliminated. There is a small error in the damage degree identification of the new indicator _Dea at unit 26. This is because the bending moment of the hyperstatic structure is redistributed after damage, but the error is small. The new indicator can identify the damage degree more accurately.

The above are only three embodiments of the present invention. All equivalent changes and modifications made according to the scope of the patent application of the present invention are within the scope of the present invention.

Claims (2)

1. A beam structure damage identification method based on deflection curvature, characterized by comprising the following steps: (1) Apply the same load to the beam structure before and after damage to obtain the measured deflection curves of the beam structure before and after damage; (2)(a) If the beam structure is statically determinate, the deflection curvature of the beam structure before and after damage is calculated, and the damage is located by the deflection curvature difference; the degree of damage is quantified by the relative change of the deflection curvature before and after damage. (b) If the beam structure is an over-determined beam structure, a set of orthogonal loads are applied to the beam structure before and after damage according to step (1), and the deflection curvature of the deflection curve of the beam structure before and after damage is calculated to obtain the deflection curvature difference under multiple loads, and the damage is located by summing the absolute value difference of the deflection curvature; the degree of damage is quantified by the absolute value and relative change of the deflection curvature of the beam structure before and after damage; In step (2), the deflection curvature w″ is calculated by central difference, and the calculation formula is as follows:

Where w is the deflection, subscript i is the measuring point number, and ε is the average value of the distance from measuring point i-1 to measuring point i and the distance from measuring point i to measuring point i+1; In step (2)(a), if the beam structure is a statically determinate beam structure, the deflection curvature difference damage location index is as follows:

Wherein, DI represents the damage location index of the statically determinate beam structure, DI _i represents the damage location index identified by the i-th measuring point of the statically determinate beam structure, w″ _iu and w″ _id are the deflection curvatures of the beam structure under load before and after damage at the i-th measuring point, respectively, and n is the number of measuring points. The measuring point No. 1 is arranged at one end of the beam structure, and the measuring point No. n is arranged at the other end of the beam structure. The number of measuring points is continuous and increases from 1 to n. i is greater than or equal to 2 and less than or equal to n-1. In step (2)(a), the quantitative calculation method of the damage degree of the beam structure is as follows: D _e = [0 D _e2 … D _ei … D _{e (n-1)} 0]; Where, _De is the quantitative index of the damage degree of the statically determinate beam structure, and _Dei is the damage degree identified at the i-th measuring point of the statically determinate beam structure; For the middle unit of the beam structure, the damage degree calculation formula is as follows:

For the edge element of the beam structure, if the rotation angle is constrained, the damage degree calculation formula is as follows:

i=2 or i=n-1; For the edge element of the beam structure, if the rotation angle is unconstrained, the damage degree calculation formula is as follows:

i=2 or i=n-1; In step (2)(b), if the beam structure is an over-determined beam structure, the specific process of damage location and quantification is as follows: For statically indeterminate beam structures, the orthogonal loads are selected so that the distance between the zero points of bending moment under each load is the largest; Select m orthogonal loads, m is greater than or equal to 2, and the absolute value difference of the deflection curvature of the beam structure before and after damage under the k load δw″ _k is shown as follows; δw″ _k ＝|w″ _dk |-|w″ _uk |＝[0|w″ _2dk |-|w″ _2uk |…|w″ _idk |-|w″ _iuk |…|w″ _{(n-1) dk} |-|w″ _(n-1)uk |0]; Wherein, w″ _uk and w″ _dk are the deflection curvatures of the indeterminate beam structure before and after damage under load k, w″ _iuk and w″ _idk are the deflection curvatures of the indeterminate beam structure before and after damage under load k at the i-th measuring point, respectively, and k is greater than or equal to 1 and less than or equal to m; The damage location is performed by taking the sum of the absolute value differences of the deflection curvature of m orthogonal loads. The calculation formula is as follows:

Where DI _a represents the damage localization index of the statically indeterminate beam structure; The quantitative calculation method of the damage degree of the statically indeterminate beam structure is as follows: D _ea = [0 D _ea2 … D _eai … D _{ea (n-1)} 0]; Where, _Dea represents the quantitative index of the damage degree of the statically indeterminate beam structure, and _Deai is the damage degree identified at the i-th measuring point of the statically indeterminate beam structure; For the middle unit of the beam structure, the damage degree calculation formula is as follows:

For the edge element of the beam structure, if the rotation angle is constrained, the damage degree calculation formula is as follows:

i=2 or i=n-1; For the edge element of the beam structure, if the rotation angle is unconstrained, the damage degree calculation formula is as follows:

i=2 or i=n-1. 2. The beam structure damage identification method based on deflection curvature according to claim 1 is characterized in that: in step (1), the measuring points of the deflection test before and after the beam structure damage are arranged in the same position, and the number of measuring points is not less than 6.

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