CN110472369B - Beam structure damage identification method for deflection curvature - Google Patents
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Abstract
The invention discloses a beam structure damage identification method of deflection curvature, which comprises the following steps: respectively applying the same load to the beam structures before and after the beam structures are damaged to obtain actually measured deflection curves of the beam structures before and after the beam structures are damaged; calculating the deflection before and after the structure is damaged, and carrying out damage positioning through the difference of the deflection and the deflection; quantifying the damage degree through the relative change of the deflection and the curvature before and after the structural damage; 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, the deflection curvature difference under the action of a plurality of loads is obtained, and the deflection curvature absolute value difference is summed to carry out damage positioning and quantification. The method can accurately position and quantify the damage of the beam structure, and is applied to the damage assessment of the beam structure.
Description
Technical Field
The invention belongs to the technical field of structural health monitoring, and particularly relates to a beam structure damage identification method for deflection curvature in a beam structure nondestructive testing technology.
Background
Structural damage identification is used as core content of a bridge health monitoring system, and identification methods are numerous. The overall damage identification method developed at home and abroad mainly comprises the following steps: a structural damage identification method based on dynamic response and static response. The dynamic response parameter index is mainly used for judging structural damage through the change of structural modes (vibration frequency and vibration mode), and the method has higher requirements on the number of measuring points, the measurement precision of a sensor, a modal parameter identification method and the like. The other method is a damage identification method based on static response parameters, the static response testing technology is simple and mature, the testing data precision is high, and the uncertain influences of quality, particularly damping and the like can be effectively avoided. The damage identification indexes based on the static response parameters mainly comprise static deflection indexes, static strain indexes, support reaction influence line indexes and the like.
The static deflection index mainly comprises a static deflection method, a deflection influence line method and a static deflection curvature method. The model of the model is used for identifying the structural unit, and the model is used for identifying the structural unit according to the structural unit, and the model is used for identifying the structural unit. Liu and so on utilize the static structure damage front and back deflection difference similar with the influence line shape that concentrated force produced in the damage unit effect, through damaging the influence line of power to discern the structural damage. The Chen Jiehao and the like perform damage identification by means of different deflection difference curves when loads are positioned in lossless and damaged areas, and the identification effect of the index is analyzed by a hollow slab example. The functional relation between the deflection difference influence line and the position of the moving load is deduced by Duyongfeng and the like, the difference of the functional relation is pointed out when the moving load is positioned in a damaged area and a lossless area, and then the damaged position is identified. And (3) fitting the deflection influence line of the structure by Zhu S Y and the like, analyzing the fitted influence line, and establishing a damage identification index by using the influence line data before and after the structural damage. And Yam and the like perform sensitivity analysis on deflection, deflection slope and damage factors of deflection curvature structures of the plate structures through a finite element model to identify structural damage. The Queen process Lin combines curvature and structural static force deflection, obtains differential curvature under static load by adopting an adjacent differential method, and identifies the damage of the single span beam by using an adjacent differential curvature difference index. Abdo researches the relation between damage characteristics and deflection curvature change, and the deflection curvature change is used as a damage index for damage identification of the structure. The Yang Cell and the like respectively provide a formula for calculating curvature by using beam structure deflection and strain, identify damage positions by using relative curvature difference before and after beam damage, and provide a static beam two-stage damage identification method based on static bending.
Although many research works are carried out on the damage positioning method of the structure based on the deflection index, the methods related to the damage degree quantification are not many, and the method for quantifying the damage degree of the structure by directly adopting static deflection curvature is rarely seen.
Disclosure of Invention
The invention provides a method for identifying the damage of a beam structure with deflection and curvature, aiming at the defect that the existing deflection and curvature method cannot identify the damage degree of the structure.
The above purpose of the invention is realized by the following technical scheme:
the method for identifying the structural damage of the beam with the deflection curvature comprises the following steps:
(1) Respectively applying the same load to the beam structures before and after the beam structures are damaged to obtain actually measured deflection curves of the beam structures before and after the beam structures are damaged;
(2) (a) if the beam structure is a static beam structure, solving the deflection curvature of the deflection curve before and after the beam structure is damaged, and carrying out damage positioning through the difference of the deflection curvature; quantifying the damage degree through the relative change of the deflection and the curvature of the beam structure before and after damage;
(b) If the beam structure is a statically indeterminate beam structure, adopting a group of orthogonal loads to act on the beam structure before and after damage according to the step (1), solving the deflection curvature of the deflection curve before and after the beam structure is damaged to obtain deflection curvature differences under the action of a plurality of loads, and carrying out damage positioning through summation of deflection curvature absolute value differences; quantifying the damage degree through the absolute value and the relative change of the deflection curvature of the beam structure before and after damage;
in the step (2), the deflection curvature w' is calculated through center difference, and the calculation formula is as follows:
in the formula, w is deflection, subscript i is a measuring point number, and epsilon is an average value of a distance between a measuring point i-1 and a measuring point i and a distance between the measuring point i and a measuring point i + 1;
in the step (2) (a), if the beam structure is a static beam structure, the deflection and curvature difference damage positioning index is shown as the following formula:
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 a damage localization index of the statically determinate beam structure, DI i Represents the damage positioning index, w ″, identified by the ith measuring point of the statically determinate beam structure iu 、w″ id The deflection curvatures of the beam structure at the ith measuring point before and after the beam structure is damaged under the action of load are respectively measured, n is the number of the measuring points, the measuring point No. 1 is 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 in sequence, and i is more than or equal to 2 and less than or equal to n-1;
in the step (2) (a), the method for quantitatively calculating the damage degree of the beam structure comprises the following steps:
D e ＝[0 D e2 … D ei … D e(n-1) 0]；
in the formula, D e Is a quantitative indicator of the damage degree of the statically determinate beam structure, D ei The damage degree identified for the ith 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 side unit of the beam structure, if the corner is constrained, the damage degree calculation formula is as follows:
for the side unit of the beam structure, if the corner is not constrained, the damage degree calculation formula is as follows:
in the step (2) (b), if the beam structure is a hyperstatic beam structure, the specific process of carrying out damage positioning and quantification is as follows:
for the statically indeterminate beam structure, the distance between the bending moment zero points under the action of each load is the largest due to the obtained orthogonal load;
selecting mOrthogonal load, m is more than or equal to 2, and the absolute value difference delta w of deflection curvature before and after the beam structure is damaged under the action of k load k As shown in the following formula;
δw″ k ＝|w″ dk |-|w″ uk |＝[0 |w″ 2dk |-|w″ 2uk | … |w″ idk |-|w″ iuk | … |w″ (n-1)dk |-|w″ (n-1)uk |0]；
in the formula, w ″) uk 、w″ dk Respectively the deflection curvature before and after the hyperstatic beam structure is damaged under the action of k load, w ″) iuk 、w″ idk Respectively the deflection curvatures before and after the statically indeterminate beam structure is damaged under the action of k load at the ith measuring point, wherein k is more than or equal to 1 and less than or equal to m;
taking the deflection curvature absolute value differences of m orthogonal loads for summation to carry out damage positioning, wherein the calculation formula is as follows:
in the formula, DI a Representing damage positioning indexes of the statically indeterminate beam structure;
the calculation method for the structural damage degree quantification of the hyperstatic beam comprises the following steps:
D ea ＝[0 D ea2 … D eai … D ea(n-1) 0]；
in the formula, D ea Quantitative index of damage degree, D, representing statically indeterminate Beam Structure eai Identifying the damage degree of the ith 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 beam structure edge unit, if the corner is constrained, the damage degree calculation formula is as follows:
for the beam structure edge unit, if the corner is not constrained, the damage degree calculation formula is as follows:
specifically, in the step (1), the positions of the measuring points of the deflection test before and after the beam structure is damaged are arranged the same, and the number of the measuring points is not less than 6.
The method applies the same load to the beam structure before and after damage to obtain the difference of deflection and curvature before and after damage of each measuring point of the beam structure, carries out damage positioning, establishes an explicit expression for calculating the damage degree according to the deflection and curvature before and after the structural damage, and can directly calculate the damage degree according to the deflection and curvature. Through the simple beam, cantilever beam and three-span continuous beam calculation examples, various damage working conditions are considered, 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 positioning and quantification.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention.
FIG. 2 is a model diagram of a single span beam structure of the present invention.
FIG. 3 is a unit force action bending moment diagram of the measuring point i-1 of the basic structure of the simply supported beam.
FIG. 4 is a unit force action bending moment diagram of the i measuring point of the basic structure of the simply supported beam.
FIG. 5 is a unit force action bending moment diagram of the measuring point i +1 of the basic structure of the simply supported beam.
FIG. 6 is a view of the external load action bending moment of the single span beam structure of the present invention.
FIG. 7 is a schematic diagram of the full-bridge uniform load of the three-span continuous beam of the invention.
FIG. 8 is a deflection diagram of a three-span continuous beam full-bridge uniform load acting structure.
FIG. 9 is a schematic view of the first span uniform load of the three-span continuous beam of the present invention.
FIG. 10 is a schematic view of the second span uniform load of the three-span continuous beam of the present invention.
FIG. 11 is a schematic view of the third span uniform load of the three-span continuous beam of the invention.
FIG. 12 is a deflection diagram of a structure with load action uniformly distributed step by a three-span continuous beam.
FIG. 13 is a schematic finite element model diagram of a simply supported beam according to an embodiment of the present invention.
Fig. 14 is a DI graph illustrating a simple beam damage localization index according to an embodiment of the invention.
FIG. 15 is a diagram illustrating a quantitative index D of damage degree of a simply supported beam in accordance with an embodiment of the present invention e Graph is shown.
FIG. 16 is a diagram of a finite element model of a second cantilever according to an embodiment of the present invention.
Fig. 17 is a DI graph of the damage localization index DI for the cantilever beam condition 1 in the second embodiment of the present invention.
Fig. 18 is a DI graph of the cantilever beam condition 2 damage localization index DI in the second embodiment of the present invention.
FIG. 19 is a quantitative index D of damage degree of the cantilever beam under working condition 1 in the second embodiment of the present invention e Graph is shown.
FIG. 20 is a quantitative index D of the damage degree of the cantilever beam under the working condition 2 in the second embodiment of the present invention e A graph.
FIG. 21 is a finite element model diagram of a three-span continuous beam according to an embodiment of the present invention.
FIG. 22 shows the damage localization index DI under condition 1 in the third embodiment of the present invention a A graph.
Fig. 23 is a DI graph of the damage localization index of working condition 1 in the third embodiment of the present invention.
FIG. 24 shows the damage localization index DI of working condition 2 in the third embodiment of the present invention a Graph is shown.
Fig. 25 is a DI graph of the damage localization index DI under condition 2 in the third embodiment of the present invention.
FIG. 26 shows the damage localization index DI of condition 3 in the third embodiment of the present invention a Graph is shown.
FIG. 27 is a quantitative index D of the degree of damage under working condition 1 in the third embodiment of the present invention ea A graph.
FIG. 28 shows the third working condition of the present invention1 quantitative index of Damage degree D e A graph.
FIG. 29 is a quantitative index D of the degree of damage under working condition 2 in the third embodiment of the present invention ea Graph is shown.
FIG. 30 is a quantitative index D of the degree of damage under working condition 2 in the third embodiment of the present invention e A graph.
FIG. 31 is a quantitative indicator D of damage level under condition 3 in the third embodiment of the present invention ea Graph is shown.
Detailed Description
The present invention is further described with reference to the following drawings and examples, wherein like reference numerals in the various figures designate identical or similar elements unless otherwise specified.
The invention relates to a beam structure damage identification method with deflection and curvature, which is realized by the following steps as shown in a flow chart in figure 1:
step 1: respectively applying the same load to the beam structures before and after the beam structures are damaged to obtain actually measured deflection curves of the beam structures before and after the beam structures are damaged;
step 2 (a): if the beam structure is a statically fixed beam structure, solving the deflection curvature of deflection curves before and after the beam structure is damaged, and carrying out damage positioning through the difference of the deflection curvatures; quantifying the damage degree through the relative change of the deflection and the curvature of the beam structure before and after damage;
step 2 (b): if the beam structure is a statically indeterminate beam structure, respectively acting a group of orthogonal loads on the beam structure before and after damage according to the step 1, solving the deflection curvature of the deflection curve before and after the beam structure is damaged to obtain deflection curvature differences under the action of a plurality of loads, and carrying out damage positioning through summation of deflection curvature absolute value differences; and quantifying the damage degree through the absolute value and the relative change of the deflection curvature of the beam structure before and after damage.
Applying the step 1, taking a single-span beam as an example, the model diagram is shown in fig. 2, the span is L, a and B are two end points of the single-span beam, the distance from the damage position to the left end is a, the damage length is epsilon, the rigidity of the undamaged beam structure is EI, and the rigidity of the damaged unit is EI d . The unit force P =1 respectively acts on the i-1 measuring point and the i and i +1 measuring points in turn to obtain the effect on each measuring pointThe bending moment diagrams at the measuring points are shown in fig. 3 to 5, and the bending moment diagram under the action of any external load q (x) is shown in fig. 6.
The bending moments under the action of unit force are respectively as follows:
in the formula (1), j represents a serial number, and when j is 1, 2 or 3,
is/are based on fig. 3 to 5 respectively>
x represents the distance from the left end point a of the beam structure.
The deflection increment before and after damage of each measuring point is respectively as follows:
in the formula, dw i Represents the deflection difference w of the i-th measuring point under the action of external load before and after the structural damage of the beam iu 、w id The deflection of the beam structure at the ith measuring point under the action of external load before and after the beam structure is damaged is respectively shown, and subscripts u and d respectively show the undamaged state and the damaged state of the beam structure.
And (3) applying the step (a), calculating the deflection curvature after the point is damaged by using a center difference method:
in the formula, w ″) iu 、w″ id Respectively shows the deflection curvature, dw ″, of the beam structure at the ith measuring point under the action of load before and after the beam structure is damaged i And (4) representing the difference of deflection curves of the beam structure at the ith measuring point under the action of loads before and after the beam structure is damaged.
Assuming that the bending moment under the action of the external load of the damage unit approximately changes in a linear relation, and the bending moment under the action of the external load of the ith measuring point is M i Then, the magnitude of the bending moment between the damaged units is as follows:
M＝M i +K(x-a) (7)；
wherein K is the slope of the change of the bending moment, and the formula (7) is substituted into the formula (6) to obtain:
when the cell between the i, i +1 measuring points is not damaged, i.e. EI d When= EI, dw ″) i ＝w″ id -w″ iu =0, i.e. the difference in deflection and curvature before and after damage is theoretically 0 at undamaged units, and dw ″, when the beam structure is damaged i Not equal to 0, so the damage can be positioned by the difference of deflection curvedness before and after damage, and the calculation method of the damage positioning 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 the formula (9), DI represents a damage localization index of the statically determinate beam structure, DI i Representing the damage positioning index identified by the ith measuring point of the statically determined beam structure, wherein n is the number of the measuring points, the curvature of the measuring point at the edge support of the beam structure cannot be calculated, and taking DI 1 ＝DI n ＝0。
Applying step 2 (a), if the edge aligning unit has a degree of freedom, such as a simple support end and a cantilever end, the bending moment at the support point is 0, that is:
M i +Kε＝0 (11)；
substituting formula (11) for formula (8):
according to mechanics of materials, the following relations exist among structural rigidity, bending moment and deflection curvature:
in the formula: ρ represents a radius of curvature and w "represents a beam structure deflection curvature.
Then the theoretical deflection curvature of the i measuring point when the beam structure is not damaged is as follows:
in formula (14), w ″) iut And (3) representing the theoretical deflection curvature of the point i when the beam structure is not damaged.
And the theoretical deflection curvature of the i measuring point when the beam structure is damaged is as follows:
in formula (15), w ″) idt And (3) representing the theoretical deflection curvature of the point i when the beam structure is damaged.
Then, the curvature of the point i can be found as:
the damage degree of the beam structure can be obtained as follows:
for the intermediate unit and the corner-constraining side supports, e.g. fixed supports, the moment increment is assumed to be small, i.e. 3M i >>K epsilon, then equation (8) is simplified to:
the theoretical damage degree can be obtained as follows:
applying the step 2 (b), for the statically indeterminate structure, taking a three-span continuous beam as an example, when uniform load loading is adopted, the deflection curve will have an inflection point, that is, a point w =0 exists, so the corresponding bending moment is also 0, at this time, the formula (13) is always true regardless of the EI value, and therefore, the index cannot identify the damage occurring at the inflection point.
Referring to fig. 7 and 8, when the uniform load is fully distributed, damage at positions of 4 inflection points (hereinafter referred to as inflection points) cannot be identified. Therefore, a step-by-step loading mode is considered for the three-span continuous beam, as shown in fig. 9 to 12, at this time, each load condition has only two inflection points, and the positions of the inflection points under the action of each load are different, and the problem that damage at the inflection 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 distance between the zero bending moment points under the action of each load is preferably maximized by the orthogonal load.
Selecting m orthogonal loads, wherein m is more than or equal to 2, and the absolute value difference delta w of deflection curvature before and after the structural damage under the action of k loads k Comprises the following steps:
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)；
wherein, w ″ uk 、w″ dk The deflection curvature before and after the hyperstatic beam structure is damaged under the action of k load, w iuk 、w″ idk Respectively the deflection curvatures before and after the statically indeterminate beam structure is damaged under the action of the load of the ith measuring point k, wherein k is more than or equal to 1 and less than or equal to m.
And (3) taking the deflection curvature absolute value differences of m orthogonal loads for summation to carry out damage positioning:
in the formula, DI a Representing damage positioning indexes of the statically indeterminate beam structure;
the calculation method of the hyperstatic structure damage degree comprises the following steps:
D ea ＝[0 D ea2 … D eai … D ea(n-1) 0] (25)；
in the formula D ea Quantitative index of damage degree, D, representing statically indeterminate beam structure eai And identifying the 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:
in formula (26), w ″) iuk 、w″ idk Respectively the k load action of the ith measuring pointDeflection curvature before and after damage of the lower statically determinate beam structure.
To the limit unit of beam structure, if the corner has the restraint, if the end is supported admittedly, then the damage degree is:
to the limit unit of beam structure, if the corner is unrestricted, like simple support end, cantilever end, then the damage degree is:
in the step 1, the positions of the measuring points of the deflection test before and after the beam 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. 13, the span of the simply supported beam is 100cm and 5cm, and is divided into 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-sectional dimension of the plate is b × h =4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 10 3 MPa, poisson's ratio of 0.37, density of 1200kg/m 3 。
Damage in actual engineered structures, such as the occurrence of cracks, corrosion of materials, or a decrease in elastic modulus, typically only causes a large change in the stiffness of the structure, with little effect on the quality 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. And (4) establishing a beam structure model by adopting the beam3 beam unit of ANSYS software. 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 Multi-damage working condition of simply supported beam
The specific implementation steps are as follows:
step 1: respectively applying uniform load of 120N/m to the simply supported beams before and after the damage to obtain the actually measured deflection curve of the simply supported beams before and after the damage.
Step 2 (lesion localization): the deflection before and after the structure is damaged is worked out to obtain the curvature, the damage is positioned through the deflection curvature difference, as shown in figure 14, the result shows that obvious peak values appear at the positions 1 and 10, DI at other undamaged positions is 0, and the index can identify all the damages.
Step 2 (injury quantification): the damage degree is quantified through the relative change of the deflection and the curvature before and after the structural damage, and the damage degree index D of the multi-damage working condition 1-2 e The identification effect is as shown in fig. 15, the index can accurately quantify the damage degree, the theoretical 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. 16, the span of the cantilever beam is 100cm and 5cm, and is divided into 20 units and 21 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 measuring point numbers). The cross-sectional dimension of the plate is b × h =4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 10 3 MPa, poisson's ratio of 0.37, density of 1200kg/m 3 。
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
The specific implementation steps are as follows:
step 1: and respectively applying 120N concentrated loads to the cantilever ends of the cantilever beams before and after the damage to obtain actual measured deflection curves before and after the damage of the cantilever beams.
Step 2 (lesion localization): the deflection before and after the structure is damaged is worked out to obtain the curvature, the damage is positioned through the difference of the deflection curvature, the damage positioning index DI identification result of the working condition 1 is shown in figure 17, the unit 1, the unit 10 and the unit 20 have unequal peak values, 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 18, the unit 1 and the unit 10 have obvious peak value bulges, the unit 1 and the unit 10 are shown to be damaged, the bulge of the free end unit 20 is smaller, and the damage can also be shown.
Step 2 (injury quantification): the damage degree is quantified through the relative change of the deflection and the curvature before and after the structural damage, and the damage quantitative indexes D of the working condition 1 and the working condition 2 e The recognition effect is similar to that of the actual damage in fig. 19 and 20, respectively.
Example three: referring to fig. 21, the span diameter of the three-span continuous beam is arranged to be 100+150+100cm,10cm to divide a unit, 35 units in total, and 36 measuring points (the numbers in the upper row of circles in the figure are the unit numbers, and the numbers in the lower row are the support numbers). The cross-sectional dimension of the plate is b × h =4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 10 3 MPa, poisson's ratio of 0.37, density of 1200kg/m 3 。
The unit 7 is located near a span bending moment 0 point (namely a deflection curvature inflection point) 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
The specific implementation steps are as follows:
step 1: the continuous beam is of a statically indeterminate structure, so that a group of orthogonal uniformly distributed loads are taken, and the uniformly distributed loads are distributed step by step as shown in fig. 9-11, namely, the uniformly distributed loads are respectively applied to all the steps by 120N/m, and an actually measured deflection curve of the continuous beam before and after damage under the action of all the loads is obtained.
Step 2 (lesion localization):calculating the deflection before and after the structure is damaged, and carrying out damage positioning by summing the absolute value differences of the deflection and the curvature, wherein the damage positioning index DI is the working condition 1 a The identification result is shown in fig. 22, the unit 7 has obvious peak value, if the full-bridge uniform load is directly adopted, the damage positioning index DI identification result of the working condition 1 is shown in fig. 23, and as can be seen, the damage position can be identified, but the peak value of the damage position has no DI a The index is obvious. Condition 2 damage location index DI a The identification result is shown in FIG. 24, and the damage localization index DI of the cell 7 at the inflection point a Obvious peak value appears, the problem that damage at the inflection point cannot be identified is avoided, damage at the inflection point can be well identified after absolute values of action indexes of uniformly distributed loads are overlapped step by step, if the full-bridge uniformly distributed loads are directly adopted, the DI identification result of the damage positioning index (DI) under the working condition 2 is shown in figure 25, and therefore, no obvious peak value appears in a unit 7, and the DI index when the uniformly distributed loads are fully distributed cannot identify damage of units near the inflection point. Working condition 3 damage location index DI a The recognition result is as shown in fig. 26, all three lesions are recognized, and the positioning effect is good. Therefore, new inflection points are generated under the action of the span-by-span uniformly distributed loads, but the positions of the inflection points generated by the uniformly distributed loads are different, and the influence of the inflection points can be avoided after indexes are superposed.
Step 2 (injury quantification): the damage degree is quantified through the absolute value and the relative change of the deflection curvature before and after the structural damage, and the damage quantitative index D is obtained under the working condition 1 ea As shown in fig. 27, the identified theoretical damage degree is slightly smaller than the actual damage degree, the error is-0.01, and a peak appears near the unit 14 at the undamaged position, so that the identification result is not affected; damage quantitative index D under working condition 1 e As a result of recognition, as shown in fig. 28, a peak appears near the cell 7, but the damage level cannot be recognized accurately.
Working condition 2 damage degree quantitative index D ea As shown in FIG. 29, the recognition effect of the damage degree of three points is good, the damage degree is almost the same as the actual value, and tiny protrusions appear at the measuring points 11 and 14 and 25, but the recognition result of the damage position does not influence the overall judgment effect of the damage degree of the index, and the damage degree D e The index is shown in FIG. 30, where there are more interference peaks, so D e The indexes cannot effectively identify the damage degree of the cell at the inflection point.
Working condition 3 damage degree quantitative index D ea The recognition effect is as shown in fig. 31, and the damage degree recognition results of the units 7 and 18 are similar to the actual damage degree. A bulge appears at the measuring point 25, but the measuring point 25 is negative because the measuring point is at a new inflection point position, and the influence of a damage degree interference peak value on the identification effect can be accurately eliminated by combining damage position identification. New indicator D at unit 26 ea The damage degree identification has small errors because the statically indeterminate structure is redistributed after being damaged in bending moment, but the errors are small, and the new index can accurately identify the damage degree.
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 of deflection curvature is characterized by comprising the following steps:
(1) Respectively applying the same load to the beam structures before and after the beam structures are damaged to obtain actually measured deflection curves of the beam structures before and after the beam structures are damaged;
(2) (a) if the beam structure is a static beam structure, solving the deflection curvature of the deflection curve before and after the beam structure is damaged, and carrying out damage positioning through the difference of the deflection curvature; quantifying the damage degree through the relative change of the deflection and the curvature of the beam structure before and after damage;
(b) If the beam structure is a statically indeterminate beam structure, adopting a group of orthogonal loads to act on the beam structure before and after damage according to the step (1), solving the deflection curvature of the deflection curve before and after the beam structure is damaged to obtain deflection curvature differences under the action of a plurality of loads, and carrying out damage positioning through summation of deflection curvature absolute value differences; quantifying the damage degree through the absolute value and the relative change of the deflection curvature of the beam structure before and after damage;
in the step (2), the deflection curvature w' is calculated through the central difference, and the calculation formula is as follows:
in the formula, w is deflection, subscript i is a measuring point number, and epsilon is an average value of a distance between a measuring point i-1 and a measuring point i and a distance between the measuring point i and a measuring point i + 1;
in the step (2) (a), if the beam structure is a statically determined beam structure, the deflection and curvature difference damage positioning index is shown as the following formula:
wherein DI represents a damage localization index of the statically determinate beam structure, DI i Represents the damage positioning index, w ″, identified by the ith measuring point of the statically determinate beam structure iu 、w″ id The deflection curvatures of the beam structure at the ith measuring point before and after the beam structure is damaged under the action of load are respectively measured, n is the number of the measuring points, the measuring point No. 1 is 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 in sequence, and i is more than or equal to 2 and less than or equal to n-1;
in the step (2) (a), the method for quantitatively calculating the damage degree of the beam structure comprises the following steps:
D e ＝[0 D e2 … D ei … D e(n-1) 0]；
in the formula, D e Is a quantitative indicator of the damage degree of the statically determinate beam structure, D ei The damage degree identified for the ith 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 side unit of the beam structure, if the corner is constrained, the damage degree calculation formula is as follows:
for the side unit of the beam structure, if the corner is not constrained, the damage degree calculation formula is as follows:
in the step (2) (b), if the beam structure is a hyperstatic beam structure, the specific process of carrying out damage positioning and quantification is as follows:
for the statically indeterminate beam structure, the distance between the bending moment zero points under the action of each load is the largest due to the obtained orthogonal load;
selecting m orthogonal loads, wherein m is more than or equal to 2, and the absolute value difference delta w of deflection curvature before and after the beam structure is damaged under the action of k load k As shown in the following formula;
δw″ k ＝|w″ dk |-|w″ uk |＝[0|w″ 2dk |-|w″ 2uk |…|w″ idk |-|w″ iuk |…|w″ (n-1)dk |-|w″ (n-1)uk |0]；
in the formula, w ″) uk 、w″ dk Respectively the deflection curvature before and after the hyperstatic beam structure is damaged under the action of k load, w ″) iuk 、w″ idk Respectively the deflection curvatures before and after the statically indeterminate beam structure is damaged under the k load action of the ith measuring point, wherein k is more than or equal to 1 and less than or equal to m;
taking the deflection curvature absolute value differences of m orthogonal loads for summation to carry out damage positioning, wherein the calculation formula is as follows:
in the formula, DI a Representing damage positioning indexes of the statically indeterminate beam structure;
the calculation method for the structural damage degree quantification of the hyperstatic beam comprises the following steps:
D ea ＝[0 D ea2 … D eai … D ea(n-1) 0]；
in the formula, D ea Quantitative index of damage degree, D, representing statically indeterminate beam structure eai To be hyperstaticThe damage degree identified by the ith measuring point of the beam structure;
for the middle unit of the beam structure, the damage degree calculation formula is as follows:
for the beam structure edge unit, if the corner is constrained, the damage degree calculation formula is as follows:
for the beam structure edge unit, if the corner is not constrained, the damage degree calculation formula is as follows:
2. The method for identifying damage to a beam structure of deflective curvature of claim 1, wherein: in the step (1), the positions of the measuring points of the deflection test before and after the beam structure is damaged are arranged the same, and the number of the measuring points is not less than 6.
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| CN106896156A (en) * | 2017-04-25 | 2017-06-27 | 湘潭大学 | By cross uniform load face curvature difference girder construction damnification recognition method |
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