GB2593851A

GB2593851A - Bearing reaction influence line curvature-based continuous beam damage identification method

Info

Publication number: GB2593851A
Application number: GB2111170.3A
Authority: GB
Inventors: Tang Shenghua; Chu Jiaqing; Zhang Xuebing; Qin Fuqian; Luo Chengfang; Jian Yu; Yang Wenxuan
Original assignee: Xiangtan University
Current assignee: Xiangtan University
Priority date: 2019-08-28
Filing date: 2020-08-07
Publication date: 2021-10-06
Anticipated expiration: 2040-08-07
Also published as: GB202111170D0; WO2021036751A1; CN110502856A; CN110502856B; GB2593851B

Abstract

Disclosed is a bearing reaction influence line curvature-based continuous beam damage identification method. The method comprises the following steps: applying a moving load to a continuous beam before and after a damage, to obtain actually measured bearing reaction influence lines of the continuous beam before and after the damage; calculating the curvatures of the bearing reaction influence lines of the continuous beam before and after the damage, and positioning the damage by means of a curvature difference of the bearing reaction influence lines; quantifying the degree of damage by means of a relative change in the curvatures of the bearing reaction influence lines of the continuous beam before and after the damage; and if the number of spans of the continuous beam is greater than two, quantifying the degree of damage by means of the sum of the absolute values of the curvatures of a plurality of bearing reaction influence lines before and after the damage. The present invention has a low requirement for the number of test points, reducing the usage number of monitoring sensors, is able to accurately position and quantify the damage of a continuous beam structure, and is applied to damage evaluation of the continuous beam structure.

Description

DAMAGE IDENTIFICATION METHOD FOR CONTINUOUS BEAM BASED ON

CURVATURES OF INFLUENCE LINES FOR SUPPORT REACTION

Field

[0001] The present invention relates to the field of structural health monitoring technology and, in particularly, to a damage identification method for a continuous beam based on curvatures of influence lines for support reaction using non-destructive testing technology of a beam structure.

Background

[0002] In recent years, more and more bridges have grown old in China, and problems arising therefrom are increasingly significant. Many existing bridges no longer meet functional requirements, and safety incidents such as bridge breakage and collapse occur from time to time. Scholars in the field of civil engineering have realized the importance of health monitoring and safety assessment of bridge structures, and have conducted research on various damage identification techniques. Structural damage identification is an important part of a health monitoring system for bridge structures. At present, there are two main types of damage identification methods. One type is a damage identification method based on dynamic parameters, which determines structural damages mainly by changes of structural modalities (vibration frequency and vibration mode). Such a method has high requirements on the number of measuring points, the measurement accuracy of sensors, modal parameter identification methods, and the like. Another type is a damage identification method based on static parameters. The structural damage identification method based on static parameters can effectively avoid uncertain influences of mass, especially damping, etc. Furthermore, current measurement equipment and technology are advanced and mature, reasonably accurate measurement values of structures can be obtained at relatively low costs. Therefore, structural damage identification technologies based on static parameters have been widely studied.

[0003] A support reaction force can represent the support condition of a continuous beam bridge, and thus can be used to directly or indirectly measure a working state of the structure. Ma Zhongjun et al. proposed a vertical support reaction index for a continuous beam bridge and provided a specific method for damage identification based on the index, pointing out that the index is not only simple to apply but also has great economic advantages. Wang Yilin et al. performed influence line analysis on a two-span continuous beam bridge, and proposed a technique using a second order difference of influence lines for support reaction as a damage localization index.

[0004] As inadequate research has been conducted on damage identification methods based on influence lines for support reaction, there are few methods for quantifying a degree of damages based on influence lines for support reaction.

Summary

[0005] An object of the present invention is to provide a damage identification method for a continuous beam based on curvatures of influence lines for support reaction, in view of the drawback that existing methods based on influence lines for support reaction cannot identify a structural degree of damages.

[0006] The damage identification method for a continuous beam based on curvatures of influence lines for support reaction described in the present invention includes steps as follows: [0007] (1) applying a moving load to the continuous beam before and after damages respectively to obtain measured influence lines for support reaction for the continuous beam before and after the damages; [0008] (2) calculating curvatures X" for the influence lines for support reaction for the continuous beam before and after the damages, and locating the damages based on curvature differences of the influence lines for support reaction, to obtain a damage localization index DI based on curvature differences of the influence lines for support reaction; and [0009] (3)(a) if the continuous beam has two spans, quantifying a degree of damages based on changes in the curvatures of the influence lines for support reaction for the continuous beam before and after the damages, to obtain a quantitative index De of the degree of damages of the beam structure, and [0010] (3)(b) if the continuous beam has three or more spans, quantifying a degree of damages based on sums of absolute values of the curvatures of the influence lines for support reaction for a plurality of supports before and after the damages, to obtain a quantitative index D" of the degree of damages of the beam structure, [0011] wherein each span of the continuous beam structure includes a plurality of segments, and each span comprises a middle segment and an end segment; [0012] wherein at step (2), the curvatures X" of the influence lines for support reaction are calculated using a central differential method by the following formula: x Xj+i -2X; + X;_1 [0013] where subscript i is a measurement point number, 6. is an average value of a distance from measurement point i-1 to measurement point i and a distance from measurement point i to measurement point 1+1 and Xi is a support reaction force when the moving load is applied at measurement point i, [0014] wherein at step (2), the damage localization index based on curvature differences of the influence lines for support reaction is expressed as: DI =[DI1 DI2 *** DI; *** DI"] =[0 X;" * * * XL -Xre * * * X;"0(1-X 1)" 0].

[0015] where DI is a damage localization index based on curvature differences of the influence lines for support reaction, DI is a damage localization index based on curvature differences of the influence lines for support reaction at measurement point i, and Xiff" and Xiffd are curvatures of the influence lines for support reaction when the moving load is applied at measurement point i before and after the damages respectively, 11 is the number of measurement points, with measurement point 1 amuiged at one end of the beam structure and measurement point n at the other end of the beam structure, the number incrementing continuously from 1 to n, and i is greater than or equal to 2 and smaller than or equal to n-1; [0016] wherein at step (3)(a), if the continuous beam has two spans, the degree of damages of the beam structure is calculated as: De= [0 De2 * * * De; *** 1)e("_1) 01.

[0017] where De is a quantitative index of a degree of damages of the beam structure, and D", is a degree of damages of the beam structure identified at measurement point I. [0018] for a middle segment of the beam structure, the degree of damages is calculated by the following formula: De, 1 X,: (2 n-1) [0019] for an end segment of the beam structure, the degree of damages is calculated by the following formula: Dee =1 (i = 2 or i = 11-1) ; 3X /d [0020] wherein at step (3)(b), if the continuous beam has three or more spans, the degree of damages of the beam structure is calculated as follows: Dec, = [0 Dea2 * * * Decei * * * De" "_1) 0[ [0021] where D,", is a quantitative index of a degme of damages of the continuous beam structure, and D"th is a degree of damages of the continuous beam identified at measurement point i, [0022] for a middle segment of the beam structure, the degree of damages is calculated by the following formula: De 1- (2 i n-1) at k I k=1 [0023] where in is the number of supports involved in the calculation, in being greater than 2 and smaller than the number of spans +I. X:dc and X:th are curvatures of the influence lines for support reaction of a support k when the moving load is applied at measurement point i before and after the damages respectively, and k is greater than or equal to 1 and smaller than or equal to in. and [0024] for an end segment of the beam structure, the degree of damages is calculated by the following formula: "eta -1 = 2 or i= n-1); tlt 3k1 2 k =1 [0025] Specifically, at step (I), locations of the measurement points for influence lines for support reaction of the beam structure are the same before and after the damages, and there are at least 6 measurement points for influence lines per span.

[0026] Specifically, at step (3), when a degree of damages at an intact location is negative, the deuce of damages is corrected by deducting, from a degree of damages at a damaged location, a degree of damages at an adjacent intact location.

[0027] Specifically, at step (3)(a). for a continuous beam with two spans. a measurement point is arranged at any one of three supports for the continuous beam to identify single-damage conditions and multiple-damage conditions of the beam structure.

[0028] Specifically, at step (3)(b), for a continuous beam with three or more spans, any two supports are selected from four or more supports for the continuous beam, and curvature indexes measured at the two supports are superimposed to avoid peaks of interference of the D, indexes at intact locations and to obtain the quantitative index D" of the degree of damages of the beam structure.

[0029] Specifically, at step (3)(b), the two supports used in the process of obtaining the quantitative index D e" of the deuce of damages of the beam structure are supports of two end spans located at both ends of the continuous beam, and a measurement point is arranged at each of the two supports of the end spans of the continuous beam to identify single-damage conditions and multi-damage conditions of the beam structure.

[0030] The present invention uses a vertical support reaction force of a structure as a research object, and proves that after damages occurs in the structure, there is an extreme value of a curvature difference between the influence lines for support reaction at the damaged location. Utilizing this characteristic, damages of the beam structure can be effectively localized and a degree of damages of the beam structure can be accurately quantified by using the curvature index. Through examples of calculation for a two-span continuous beam and a three-span continuous beam, the multiple-damage conditions of the beam structure arc analyzed, and value of curvature index of influence lines for support reaction in beam structure damage identification is verified, and a new effective method of beam structure damage localization and quantification is provided.

Brief Description of the Drawings

[0031] Fig. 1 is a flow block diagram of a method of the present invention.

[0032] Fig. 2 is a structural model diagram of a two-span continuous beam of the present invention.

[0033] Fig. 3 is a bending moment diagram of unit force action of a basic structure B support of a simply supported beam of the present invention.

[0034] Fig. 4 is a bending moment diagram of external load action of a two-span continuous beam of the present invention [0035] Fig. 5 is a finite element model diagram of a two-span continuous beam in embodiment 1 of the present invention.

[0036] Fig. 6 shows a curve graph of damage localization indexes DI in a single-damage conditions 1 in embodiment 1 of the present invention.

[0037] Fig. 7 shows a curve graph of damage localization indexes DI in a single-damage conditions 2 in embodiment 1 of the present invention.

[0038] Fig. 8 shows a curve graph of damage localization indexes DI in a single-damage conditions 3 in embodiment 1 of the present invention.

[0039] Fig. 9 shows a curve graph of damage localization indexes DI in a single-damage conditions 4 in embodiment 1 of the present invention.

[0040] Fig. 10 shows a curve graph of degree of damages quantitative indexes De in a single-damage conditions 1 in embodiment 1 of the present invention.

[0041] Fig. 11 shows a curve graph of degree of damages quantitative indexes De in a single-damage conditions 2 in embodiment I of the present invention.

[0042] Fig. 12 shows a curve graph of degree of damages quantitative indexes De in a single-damage conditions 3 in embodiment 1 of the present invention.

[0043] Fig. 13 shows a curve graph of degree of damages quantitative indexes De in a single-damage conditions 4 in embodiment 1 of the present invention.

[0044] Fig. 14 is a schematic diagram of degree of damages correction in embodiment 1 of the present invention.

[0045] Fig. 15 shows a curve graph of damage localization indexes DI in a multiple-damage condition 1 in embodiment 1 of the present invention.

[0046] Fig. 16 shows a curve graph of deuce of damages quantitative indexes De in a multiple-damage condition 1 in embodiment 1 of the present invention.

[0047] Fig. 17 shows a curve graph of damage localization indexes DI in a multiple-damage condition 2 in embodiment 1 of the present invention.

[0048] Fig. 18 shows a curve graph of deuce of damages quantitative indexes De in a multiple-damage condition 2 in embodiment 1 of the present invention.

[0049] Fig. 19 is a finite element model diagram of a three-span continuous beam in embodiment 2 of the present invention.

[0050] Fig. 20 shows a curve graph of damage localization indexes DI in a single-damage conditions 1 in embodiment 2 of the present invention.

[0051] Fig. 21 shows a curve graph of deuce of damages quantitative indexes De in a single-damage conditions 1 in embodiment 2 of the present invention.

[0052] Fig. 22 shows a curve graph of damage localization indexes DI in a single-damage conditions 2 in embodiment 2 of the present invention.

[0053] Fig. 23 shows a curve graph of a degree of damages quantitative index De of a support 1# in a single-damage condition 2 in embodiment 2 of the present invention.

[0054] Fig. 24 shows a curve graph of a degree of damages quantitative index De of a support 2# in a single-damage condition 2 in embodiment 2 of the present invention.

[0055] Fig. 25 shows a curve graph of a degree of damages quantitative index De of a support 3# in a single-damage condition 2 in embodiment 2 of the present invention.

[0056] Fig. 26 shows a curve graph of a degree of damages quantitative index De of a support 4# in a single-damage condition 2 in embodiment 2 of the present invention.

[0057] Fig. 27 shows a curvature graph of a reaction influence line of a support 1# in a single-damage condition 2 in embodiment 2 of the present invention.

[0058] Fig. 28 shows a curve graph of superimposition of degree of damages quantitative indexes De, of supports 1# to 4# in a single-damage condition 2 in embodiment 2 of the present invention.

[0059] Fig. 29 shows a curve graph of superimposition of degree of damages quantitative indexes Dea of supports 1# and 2# in a single-damage condition 2 in embodiment 2 of the present invention.

[0060] Fig. 30 shows a curve graph of superimposition of degree of damages quantitative indexes Dea of supports 1# and 3# in a single-damage condition 2 in embodiment 2 of the present invention.

[0061] Fig. 31 shows a curve graph of superimposition of degree of damages quantitative indexes De, of supports 1# and 4# in a single-damage condition 2 in embodiment 2 of the present invention.

[0062] Fig. 32 shows a curve graph of superimposition of degree of damages quantitative indexes De" of supports 2# and 3# in a single-damage condition 2 in embodiment 2 of the present invention.

[0063] Fig. 33 shows a curve graph of superimposition of degree of damages quantitative indexes Den of supports 2# and 4# in a single-damage condition 2 in embodiment 2 of the present invention.

[0064] Fig. 34 shows superimposition of degree of damages quantitative indexes De, of supports 3# and 4# in a single-damage condition 2 in embodiment 2 of the present invention.

[0065] Fig. 35 shows a curve graph of damage localization indexes DI in a single-damage conditions 3 in embodiment 2 of the present invention [0066] Fig. 36 shows a curve graph of superimposition of degree of damages quantitative indexes De" of supports 1# and 3# in a single-damage condition 3 in embodiment 2 of the present invention.

[0067] Fig. 37 shows a curve graph of superimposition of degree of damages quantitative indexes De, of supports 1# and 4# in a single-damage condition 3 in embodiment 2 of the present invention.

[0068] Fig. 38 shows a curve graph of damage localization indexes DI in a multiple-damage condition 1 in embodiment 2 of the present invention.

[0069] Fig. 39 shows a curve graph of superimposition of degree of damages quantitative indexes D," of supports 1# and 4# in a multiple-damage condition 1 in embodiment 2 of the present invention.

[0070] Fig. 40 shows a curve graph of damage localization indexes DI in a multiple-damage condition 2 in embodiment 2 of the present invention.

[0071] Fig. 41 shows a curve graph of superimposition of degree of damages quantitative indexes D" of supports 1# and 4# in a multiple-damage condition 2 in embodiment 2 of the present invention.

Detailed Description of the Embodiments

[0072] The present invention is further described below in conjunction with the accompanying drawings and embodiments. In the description, same numerals in different drawings represent same or similar elements, unless otherwise indicated.

[0073] A damage identification method for a continuous beam based on curvatures of influence lines for support reaction described in the present invention, a flow diagram of which is shown in Fig. 1, specifically includes steps as follows.

[0074] Step 1: applying a moving load to the continuous beam before and after damages, respectively, to obtain measured influence lines for support reaction of the continuous beam before and after the damages; [0075] Step 2: for the influence lines for support reaction of the continuous beam before and after the damages, calculating curvatures of the influence lines for support reaction, and locating the damages based on curvature differences of the influence lines for support reaction; [0076] Step 3: (a) in the case of a two-span continuous beam, quantifying a degree of damages by changes in curvatures of the influence lines for support reaction of the continuous beam before and after the damages; [0077] (b) in the case of a three-or-more-span continuous beam, quantifying a degree of damages by the sum of absolute values of curvatures of reaction influence lines of a plurality of supports before and after the damages.

[0078] At step 1, using a two-span continuous beam as an example for theoretical analysis, as shown in Fig. 2, A, B and C represent three supports, i.e., a left support, a middle support and a right support; with a reaction force of the middle support B as a basic unknown quantity X. an external force P moves from a left end to a right end, and a displacement of the beam structure is assumed to be caused by the bending deformation of the structure only. The distance from the damaged location to support A is a, the damages length is e, the distance from the moving load to support A is X, the lengths of both spans are L, the stiffness of an intact part of is El, and the stiffness of a local damages element is hid. The reaction influence line of the middle support B is derived by using a force method and a curve graph multiplication method.

[0079] Now assuming that the damaged location is in the interval [a. LJ and the moving load moves in the interval [0, a], the following basic equation can be established by the force method: 811X + A, =0 (1); [0080] in equation (1). X is a support reaction force of the middle support B; is a displacement under the action of a unit force alone; Alp is a displacement of the basic structure in a direction vertical to X under the action of the load alone.

[0081] To calculate 1511 and,A11" bending moment diagrams M1 (x) and m 2 (x) of the basic structure under the action of the moving load P and bending moment diagrams (x) and M2 (x) under the action of the unit force are drawn. The diagrams M1(x) and M2 (X) of the basic structure are shown in Fig 3, and the diagrams MI (x) and M, (x) are shown in Fig. 4. M, (x) (X) [0082] Expressions of the bending moment diagrams action of the unit force are: and - under the (2); M1(x) M2 (x) of [0083] expressions of the bending moments and any cross-section under the action of the moving load P are: 2L- Px x E [0,T] 2L M2(x)= 2 (2L-x) xE(.7,21,1 2L (3); [0084] when the beam structure is not damaged, calculation is performed by the graph multiplication method to obtain: I. A iL (X) Al; () 1 /1 21. / M2CON12(x)dx L' (4); (511" = -dX -x-dx + j. j-D 4 L--x _ -- (5); ° m,(x)A42(x)dx 2 (Ix Alpu +12' El ( El El 6E1 A4,(x)m,00 ± Jo El 1- EI El 3L-12Elk (6); [0086] in the formula, the subscript "u" indicates the intact state; Xm (7) represents a reaction force of support B in the intact state when the moving load acts on a position at a distance 7 c [0,L1 from support A. [0087] When the beam structure is damaged, calculation is performed by the graph multiplication method to obtain: -El0 + fa als /14:(x)dr + if I;(x)dx+-1 AT(x)dx " El a s El L 1 if, \,3 = 1 (2L3 +a -(a + )+-a + 7 -12EI 12E18 { M (x)= ix x e [0, Li 11/12(x)=-1(2L-x) xE(L,2L] [0085] a vertical support reaction force of the middle support B in an intact state is A 6E1 FT X"(I)= l= , (3L2 -72) = (3L2 1; 12E1 21: (7); A= - 1 1 Al 1(x)111,(x)tit -Elf° IQ, (xxix +-El -17 fil WM20)th + El,-1 L + Ml(x)M2(x)th + El El - 3L? 1 1 \ (3a2 s +3as2 + 83 -6Las -3L82) + --El El El 12E1 121. (8); A 1 pd (9); 811d [0088] in the formula, the subscript "d" indicates a damaged state; "Km (7) represents a reaction force of support B in the damaged state when the moving load acts on a position at a distance 7 E [0' a] from support A; [0089] therefore, a difference of the influence lines for support reaction of the continuous beam before and after the damages is: dX,(7)= X,(?) - (E1 -El").7[(3a2 +3as + 62)(72 -5L2) + 6E3 (2a + s) 2L3 [2L30, + (E/ -ET, )(302 +3de +els] (10); dX i(i) [0090] in the formula, represents a reaction force difference of support B before and after the damages when the moving load acts on a position at a distance 7 E [0, a 1 from support A. [0091] Similarly, a difference of the influence lines for support reaction when the load P is located to the right of the first-span damages interval E [a + S. L]) can be calculated: Ps (E/ -Eid)(L - -Lx + 4L2 (3a2 + 3cts + 6.2) (7) = X rd (7) -X 11(7. ) - 21,3[21-.3 El d +(El -El d)(3a2 +3a6 + £2 £1 dX Jr) [0092] in the formula, represents a reaction force difference of support B before and after the damages when the moving load acts on a position at a distance x E [a + LiX (Y) from support A; and represents a reaction force of support B in the L] damaged state when the moving load acts on a position at a distance x E [a + c, from support A; [0093] in application of step 2, curvatures of the influence lines for support reaction in the intact state can be obtained from equation (6): (1 I);

U

rt._ 3 Xiii(x)= -(12); [0094] in (he foimula, Xl(k) represents a curvature of the reaction influence line of support B in the intact state when the moving load acts on a position at a distance -e [0, Li from support A. [0095] For the damaged state, when the load P acts on a measurement point i-1 on the left side of the damaged location, on a measurement point i on the right side of the damaged location, and on a measurement point i-Fl at a distance a from measurement point i, respectively, reaction forces of support B are respectively: X(i i)d = X "(a) + dX i(a) (13); Xid = X "(a + s)+ (IX r(a + s) (14); X (i+nd = X " (a + 20+ dX (a + 2c) (15); [0096] a curvature corresponding to measurement point i on the right side of the damaged location can be calculated using a central difference method: X+(i 11)d -2Xid Xlt 1)d X fr 3P(a + 6) -(El -El d)[-111 (3a +28)+36'4 +3a5 (3a2 + 605 + 452) 3(a + 0[2E3E1 d + (El -El d)(3a2 +3ac + 62) 61 -+1 (16); [0097] curvatures of the influence lines for support reaction before the damages when the moving load is applied at measurement point i are: -3P (a + L3 [0098] when no element between the left and right measurement points is damaged, that X"-X" =0 is, when Eld=0, , which means that theoretically a curvature difference of the support damages reaction influence line before and after the damages at the intact element is 0, thus damage identification can be performed in this case by using the curvature difference of the influence lines for support reaction as an index. A damage localization index is calculated as follows: DI =[DI I DI, * * * DI, * * * 01,_, DI "] = [0 X -X ci, X -X * * X -X 0] (18); (17); [0099] where DI is a damage localization index based on curvature differences of the influence lines for support reaction; Die is a damage localization index based on curvature differences of the influence lines for support reaction at measurement point i; and Xi: and X111 are respectively curvatures of the influence lines for support reaction before the structural damages when the moving load is applied at measurement point i, n is the number of measurement points, a measurement point 1 is arranged at one end of the beam structure, a measurement point /2 is arranged at the other end of the beam structure, the numerals of measurement points are continuous from 1 to n in increasing order, and i is greater than or equal to 2 and smaller than or equal to n-1; [00100] in application of step 3(a), for a two-span continuous beam, a degree of damages of the beam structure is calculated as follows: D" = [o De2 * * * De, * * De(."_,e) 0] (19); [00101] in the formula, De is a quantitative index of a degree of damages of the beam structure; and Deis a degree of damages of the beam structure identified at measurement point i; [00102] for a middle element of the beam structure, the degree of damages is calculated by the following formula: L3 [00103] only the relevant large terms of are retained while ignoring terms with relatively small values, and equation (16) can be.\\ reduced to: (20); id itt El 3a +2c +1 _\ Eld)6(a + e)

-

[00104] the following can be calculated: El + 8) Xirid _6(a 1+1 Eld 3a + 2c ^,X -1 (21); [00105] hence, the degree of damages of the beam is: Elp; =1--EId =1 EI 6(a + s) ( +1 Xiffd 1 3a +26. (22);

[00106] assuming that a is relatively small, equation (22) is reduced to D =1- (2 n-1) 2 id 1 x7 i (23); [00107] for an end segment of the beam structure, a=0, and equation (22) is reduced to: (i = 2 or i = n-1) (24); [00108] in application of step (3)(b), for a three-or-more-span continuous beam, the degree of damages of the beam structure is calculated as follows: Dec/ = [0 De,42 * * * Deai * * * De" _1, 01 (25); [00109] in the formula, Dee is a quantitative index of a degree of damages of the three-or-more-span continuous beam structure; and Deai is a beam structure degree of damages of the three-or-more-span continuous beam identified at measurement point i.

[00110] For a multi-span continuous beam with the more than two spans, the existence of zero points in curvatures of reaction influence lines of supports leads to abnormal interference peaks in the indexes De of the reaction influence lines of the supports, but the interference peaks of the supports are different, and in this case, the degree of damages is calculated by superimposing absolute values of the reaction influence curvatures of the supports.

[00111] for a middle element of the beam structure, the degree of damages is calculated by the following formula: De, -1- (2 i I) 2 k-1 k=1 (26); [00112] In the formula, In is the number of supports involved in the calculation, in is greater than 2 and smaller than the number of span +1, Xk and ha are respectively curvatures of the influence lines for support reaction of a support k before and after the damages of the beam structure when the moving load is applied at measurement point i, and k is greater than or equal to 1 and smaller than or equal to In.

[00113] For an end segment of the beam structure, the degree of damages is calculated by the following formula: D", -1- 1 (i = 2 or i = n -1) (27). II7

Ixrdk I 3 k -1 2 In k =1 [00114] At step 1, the arrangements of locations of measurement points for influence lines for support reaction test before and after the damages of the beam structure are same, and there are not less than 6 measurement points per span for the influence line.

[00115] At step 3, when a degree of damages at an intact location is negative, the degree of damages is corrected by reducing, from a degree of damages value at a damaged location, a degree of damages value at an adjacent intact location [00116] Embodiment I: Referring to Fig. 5, an organic glass plate model is used to simulate a two-span continuous beam with a span arrangement of 50+50cm, divided into a total of 20 elements by 21 measurement points, with each element being 5cm (in the figure, numerals in an upper row of circles are element numbers, numerals in a lower row are support numbers, and numbers of a measurement point on the left and a measurement point on the right side of an element i are i and i+1, respectively). Cross-sectional dimensions are bxh=4.5cmx1.5cm, the elasticity modulus of material is 2.7x103MPa, the Poisson's ratio is 0.37, and the density is 1200kg/m3.

[00117] Damages in actual engineering structures, such as the generation of cracks, material conosion or reduction in elastic modulus, generally only causes a large change in structural stiffness and has a small effect on the mass of the structure. Therefore, in finite element calculation, it is assumed that the structural element damages only cause a decrease in dement stiffness, but not a change in element mass. The element damages are simulated by the reduction of the elastic modulus.

[00118] 1) Single-damage situations [00119] Damages of an end segment 1 and a middle element 15 of the second span are considered respectively, with damages working conditions shown in Table 1.

[00120] Table 1 Single-damage conditions of a two-span continuous beam Working condition 1 2 3 4 Reduction in stiffness of Element 1 10 30 10 30 damaged element/go Element 15 [00121] Step 1: applying a moving load of 120N to the continuous beam before and after damages, respectively, to obtain measured influence lines for support reaction of the continuous beam before and after the damages.

[00122] Step 2: calculating curvatures of the influence lines for support reaction of the continuous beam before and after the damages, and locating the damages based on curvature differences of the influence lines for support reaction. Identification effects of DI indexes of supports 1# to 3# under working condition 1 are shown in Fig. 6, with peaks of different degrees appearing at element 1, indicating that the damages occur at element 1. The DI indexes of supports 1# to 3# can all be used to achieve accurate identification of the damages. Since supports 1# and 3# are symmetrical, their identification effects are same, and the identification peak of support 2# is the highest. Identification effects of DI indexes under working condition 2 are shown in Fig. 7, with peaks appearing at element I. In this case, the DI index of each support can be used to identify the damages of element 1, and the DI index identification peak of support 2# is the highest. Identification effects of indexes under working condition 3 are shown in Fig. 8, with peaks of DI indexes of supports 1# to 3# appearing at element 15, the identification effects of supports 1# and 3# are same, and the damages occurs at element 15. Identification effects of DI indexes under working condition 4 are good, as shown in Fig. 9, with peaks appearing at element 15, indicating that the damages occur at element 15, and the identification index peak of support 2# is the highest.

[00123] Step 3: quantifying a degree of damages by changes in curvatures of the influence lines for support reaction of the continuous beam before and after the damages. De identification indexes under working condition 1 are shown in Fig. 10. Supports 1# to 3# can all achieve accurate identification of the damages at the end segment 1, and theoretical degree of damages identified by the indexes are same as an actual degree of damages. In this case, a measurement point can be arranged at any one of supports 1# to 3# to identify the damages of the working condition 1, thus greatly optimizing the arrangement of sensors. De identification indexes under working condition 2 are shown in Fig. 11. When large damages occur at the end segment 1, the De indexes of support 1# to 3# can also achieve accurate identification of the damages. In this case, a measurement point can be arranged at any one of the supports to identify the damages. Identification effects of De indexes under working condition 3 are shown in Fig. 12. The indexes of supports 1# to 3# achieve same identification effects, and theoretical degree of damages identified thereby are close to an actual degree of damages. In this case, a measurement point can also be arranged at any of supports 1# to 3# to identify the damages. Degree of damages identification indexes De under working condition 4 are shown in Fig. 13. The results show that the theoretical degree of damages identified under working conditions 3 and 4 are lower than actual degree of damages because the De indexes at intact locations are all negative and have large values. In this case, a method shown in Fig. 14 can be used to perform correction by reducing a De value of an adjacent intact location from a De value of a damaged location, and calculating an average value of De values of a left measurement point and a right measurement point to obtain a final degree of damages De= (Dt+Dc)12. Degree of damages identification values under working conditions 3 and 4 are 0.092 and 0.277 respectively before correction, and change to 0.102 and 0.317 respectively after correction. It can be seen the degree of damages after correction are closer to actual values.

[00124] In summary, the DI indexes of supports 1# to 3# can all achieve localization of a single damages, indicating that the DI indexes are relatively sensitive to a single damages, and the theoretical degree of damages identified by the De indexes are all close to the actual degree of damages, and there are small errors because in the theoretical derivation process, to simplify the operation, terms that have small influences on the result are ignored, and values are approximated to cause errors, but this does not affect the actual damage identification effects. For the identification of a single damages, localization and quantification for damage identification can be achieved by arranging a measurement point at any of supports 1# to 3#, thus greatly reducing the number of sensors and the difficulty of sensor arrangement.

[00125] 2) Multiple-damage situations [00126] Damages of an end segment 1 and a middle element 15 of the second span are considered, and the two elements are assumed to have damages to different degrees, with damages working conditions shown in Table 2.

[00127] Table 2 Multiple-damage conditions of a two-span continuous beam Working condition 1 2 Reduction in damaged Element 1 30 30 element stiffnessa Element 15 30 10 [00128] Identification by DI indexes under working condition 1 is shown in Fig. 15, with obvious bulges appearing at an end segment 1 and an element 15, and the indexes can be used to achieve excellent identification of all damages. Identification by degree of damages indexes D, under working condition 1 is shown in Fig. 16, with peaks appearing at both the end segment 1 and element 15, and the De indexes of three supports can all achieve accurate quantification of degree of damages of element 1 and element 15. A support reaction curvature corresponding to measurement point 21 is zero, resulting in a bulge, and a small peak appears there, which does not affect an actual identification result.

[00129] Due to the complexity of damages in actual engineering, a mixed condition such as a working condition 2 in Table 2 is considered. When different elements are damaged to different degrees, a DI index still has a good identification effect, as shown in Fig. 17, in which peaks of different degrees appear at the end segment 1 and element 15, indicating damages thereof, and there are no interference peaks. Identification effects of degree of damages De indexes are shown in Fig. 18, theoretical degree of damages identified by the indexes are close to an actual degree of damages. In summary, the indexes of supports 1# to 3# have good identification effects, and can achieve localization and quantification by identifying all the damages of the structure, without missing any damages, so all single-damage and multiple-damage conditions can be identified by arranging a measurement point at any of supports 1# to 3#.

[00130] Embodiment 2: Similarly an organic glass plate model is used to simulate a three-span continuous beam, as shown in Fig. 19, with a span arrangement of 50+75+50cm, divided into a total of 35 elements by 36 measurement points, with each element being 5cm (in the figure, numerals in an upper row of circles are element numbers, numerals in a lower row are support numbers, and numbers of a measurement point on the left and a measurement point on the right side of an element i are i and i+1, respectively). For cross-sectional dimensions and material parameters, please refer to the calculation example of the two-span continuous beam.

[00131] 1) Single-damage situation [00132] Damages conditions are shown in Table 3, wherein an element 1 is located near a support 1# at the left end of the first span, an element 18 is a midspan element in the middle span, and an element 26 is located near a support 3# at the left end of a part with the largest negative moment in the third span.

[00133] Table 3 Single-damage conditions of a three-span continuous beam Working condition 1 2 3 Element 1 10 Reduction in stiffness of damaged elementa Element 18 10 Element 26 30 [00134] Di indexes under working condition 1 are shown in Fig. 20, with obvious peaks of the DI indexes of supports 1# to 4# appearing at element 1, and the DI indexes can achieve accurate identification of a small damages at an end segment. De identification indexes are shown in Fig. 21, and the De indexes of supports 1# to 4# can all achieve accurate identification of a degree of damages. DI indexes under working condition 2 are shown in Fig. 22, with obvious peaks of the DI indexes of supports 1# to 4# appearing at element 18, indicating that the indexes can all achieve accurate identification of a damages, and the peaks of the DI indexes of supports 1# to 4# are substantially equal as element 18 is located at a midspan position. De indexes of supports 1# to 4# under working condition 2 are shown in Figs. 23-26, respectively, and the De indexes of the supports can all achieve accurate identification of a degree of damages, but the De indexes of the supports have interference peaks of different degrees due to zero points for curvatures of influence lines for support reaction of supports 1#-4# before and after the damages. For example, using support 1# as an example, as shown in Fig. 27, 0 points appear at measurement points 22 and 23, and the term in the denominator of formula (23) causes abnormal bulges of the interference peaks, which are liable to interfere with the degree of damages identification or even cause damages misjudgment. As the interference peaks of the De indexes of supports 1# to 4# are different, the indexes of supports 1# to 4# are superimposed to calculate a new Dee index so as to offset their effects.

[00135] An identification effect of a D" index obtained by superimposing the indexes of supports 1# to 4# under working condition 2 is shown in Fig. 28. A theoretical degree of damages identified by the index is close to an actual degree of damages, and there is no interference peak, but a measurement point needs to be arranged at each support, and more data need to be processed, which is not convenient for calculation. Therefore, consider superimposing as few indexes as possible to identify a degree of damages. An identification effect of a D," index calculated by superimposing the indexes of supports 1# and 2# is shown in Fig. 29. In this case, a small interference peak appears at a measurement point 20, and the difference between values of the De" index at a measurement point 17 and a measurement point 18 is large, so the effect is poor. Identification by a De" index obtained by superimposing the indexes of supports 1# and 3# is shown in Fig. 30, in which a theoretical degree of damages is close to the actual degree of damages, so the effect is good. Identification by a De" index obtained by superimposing the indexes of supports 1# and 4# is shown in Fig. 31, in which the D," index shows a downward shift at measurement points near the damaged element, but a corrected degree of damages of 0.1015 is very close to an actual value. D" obtained by superimposing the indexes of supports 2# and 3# is shown in Fig. 32, and achieves a same effect as superimposing supports 1# and 4#. Dea obtained by superimposing the indexes of supports 2# and 4# is shown in Fig. 33, and achieves a same effect as superimposing supports 1# and 4#. Dea obtained by superimposing the indexes of supports 3# and 4# is shown in Fig. 34, in which a theoretical degree of damages identified by the index is close to the actual degree of damages, but the difference between values at measurement points on the left and right sides of the damaged element 18 is large.

[00136] In summary, the DI index can identify single-damage situations at all locations of three-span beam elements, and the single-damage identification index has no interference peak. The theoretical degree of damages under the identification index is very dose to the actual degree of damages. For an interference peak of the D, index at an intact location, its influence can be avoided by merely superimposing the indexes of two supports. As support 2# and support 3# are close to each other, and support 3# and support 4# are close to each other, which are liable to generate concentrated peaks, thus the indexes of support 1# and support 3#, the indexes of support 1# and support 4#, or the indexes of support 2# and support 4# can be superimposed, thereby optimizing the arrangement of sensors. Due to the limitation of space, in the following description, only the indexes of support 1# and support 3#, and the indexes of support 1# and support 4# are superimposed respectively for degree of damages identification.

[00137] DI indexes of a working condition 3 are shown in Fig. 35, with peaks appearing at an element 26, and the DI indexes of supports 1# to 4# can identify the damages. Identification results of De" obtained by superimposing the indexes of supports 1# and 3#, and superimposing the indexes of supports 1# and 4# are shown in Figs. 36 and 37, wherein the index Dea obtained by superimposing the curvature indexes of supports 1# and 3# before and after the damages shows a small peak at a measurement point 15, and the index Dca obtained by superimposing the curvature indexes of supports 1# and 4# before and after the damages has a relatively good identification effect because the distance between the two end span supports is the largest, such that the locations of interference peaks are not concentrated, so the superimposition of the curvature indexes of the two end span supports can maximally cancel out the interference peaks, and no interference peak is generated, but a theoretical degree of damages identified by the index is slightly greater than an actual degree of damages, with an error of +0.05. In summary, for the multi-span continuous beams, all single-damage situations can be identified by arranging a measurement point at each of the two side supports in the end spans.

[00138] 2) Multiple-damage situations [00139] In multiple-damage conditions of the three-span continuous beam, damages of different degrees of dements 1, 18 and 26 are considered, with the damages working conditions shown in Table 4.

[00140] Table 4 Multiple-damage conditions of a three-span continuous beam Working condition 1 2 Element 1 30 30 Reduction in stiffness of Element 18 30 10 damaged element/% Element 26 30 20 [00141] DI indexes of supports 1# to 4# under working condition 1 are shown in Fig. 38, in which the damage identification indexes of support 1# to 4# have obvious peaks at elements 1, 18 and 26, and can be used to identify all the damages. De indexes of supports 1# to 4# under working condition 1 can be used to identify all the damages, but there are interference peaks. In this case, the curvature indexes of support 1# and support 4# are superimposed to obtain a new Dea index, as shown in Fig. 39, which can filter out the interference peaks and accurately identify the degree of damages, and the Dea index has errors of ± 0.05 error at element 18 and element 26.

[00142] DI indexes under working condition 2 are shown in Fig. 40, with obvious peaks appearing at elements 1, 18 and 26, and the indexes can accurately identify the damages. Indexes of support 1# and support 4# under working condition 2 are superimposed to obtain a new D" index, as shown in Fig. 41, in which atheoretical degree of damages at element 26 is slightly greater than an actual degree of damages, but the error is insignificant, so the index can be used to relatively accurately identify the degree of damages.

[00143] Described above are only two embodiments of the present invention, and all equivalent variations and modifications made in accordance with the scope of the patent claims of the present invention are covered by the present invention.

Claims

CLAIMS1. A damage identification method for a continuous beam based on curvatures of influence lines for support reaction, comprising the following steps: (1) applying a moving load to the continuous beam before and after damages respectively to obtain measured influence lines for support reaction for the continuous beam before and after the damages; (2) calculating curvatures X" for the influence lines for support reaction for the continuous beam before and after the damages, and locating the damages based on curvature differences of the influence lines for support reaction, to obtain a damage localization index DI based on curvature differences of the influence lines for support reaction; and (3)(a) ii the continuous beam has two spans, quantifying a degree of damages based on changes in the curvatures of the influence lines for support reaction for the continuous beam before and after the damages, to obtain a quantitative index D. of the degree of damages of the beam structure, and (3)(b) if the continuous beam has three or more spans, quantifying a degree of damages based on sums of absolute values of the curvatures of the influence lines for support reaction for a plurality of supports before and after the damages, to obtain a quantitative index D" of the degree of damages of the beam structure, wherein each span of the continuous beam structure includes a plurality of segments, and each span comprises a middle segment and an end segment; wherein at step (2), the curvatures X" of the influence lines for support reaction are calculated using a central differential method by the following formula: X1 -2Xi + Xj_1 where subscript i is a measurement point number, 6. is an average value of a distance from measurement point i-1 to measurement point i and a distance from measurement point i to measurement point i+1, and Xi is a support reaction force when the moving load is applied at measurement point wherein at step (2), the damage localization index based on curvature differences of the influence lines for support reaction is expressed as: DI =[DI1 DI2 * * * DI1 * * * DIn_i DI,,] =[0 X41,2 -X * * * X i72 -X * * * X [1,,_ 1 jcl n-Ou where DI is a damage localization index based on curvature differences of the influence lines for support reaction. DI is a damage localization index based on curvature differences of the influence lines for support reaction at measurement point i, and AC and Xlid are curvatures of the influence lines for support reaction when the moving load is applied at measurement point i before and after the damages respectively, n is the number of measurement points, with measurement point 1 arranged at one end of the beam structure and measurement point ii at the other end of the beam structure, the number incrementing continuously from 1 to n, and i is greater than or equal to 2 and smaller than or equal to n-1; wherein at step (3)(a), if the continuous beam has two spans, the degree of damages of the beam structure is calculated as: D, = [() De2 * * * De, 1e("_0 where De is a quantitative index of a degree of damages of the beam structure and is a degree of damages of the beam structure identified at measurement point i, for a middle segment of the beam structure, the degree of damages is calculated by the following formula: Do =1 1 (2 i n-1) xz, and for an end segment of the beam structure, the degree of damages is calculated by the following formula: De, -1- (i = 2 or i = n -1); 3 'd 2 Xi: wherein at step (3)( b), if the continuous beam has three or more spans, the degree of damages of the beam structure is calculated as follows: D" = [1:1) D"2 * * * D"i * * * De"(n_1) where Dei, is a quantitative index of a degree of damages of the continuous beam structure, and De" is a degree of damages of the continuous beam identified at measurement point i, for a middle segment of the beam structure, the degree of damages is calculated by the following formula: Dem =1 1 Jr, L1xL1 2k1 1 IIACCk I A-1 where in is the number of supports involved in the calculation, in being greater than 2 and smaller than the number of spans +1. Xiffuk and ulk are curvatures of the influence lines for support reaction of a support k when the moving load is applied at measurement point i before and after the damages respectively, and A is greater than or equal to 1 and smaller than or equal to In, and for an end segment of the beam structure, the degree of damages is calculated by the following formula: Deco =1- rn (i=2 or i = n -1) . XIk 3k1 2 in Iv I k=1 2. The method of claim 1, wherein at step (1), locations of the measurement points for influence lines for support reaction of the beam structure are the same before and after the damages, and there are at least 6 measurement points for influence lines per span.3. The method of claim 1, wherein at step (3), when a degree of damages at an intact location is negative, the degree of damages is corrected by deducting, from a degree of damages at a damaged location, a degree of damages at an adjacent intact location.4. The method of claim 1, wherein at step (3) (a), for a continuous beam with two spans, a measurement point is arranged at any one of three supports for the continuous beam to identify single-damage conditions and multiple-damage conditions of the beam structure.5. The method of claim 1, wherein at step (3)(b), for a continuous beam with three or more spans, any two supports are selected from four or more supports for the continuous beam, and curvature indexes measured at the two supports are superimposed to avoid peaks of interference of the D" indexes at intact locations and to obtain the quantitative index D" of the degree of damages of the beam structure.6. The method of claim 5, wherein the two supports used in the process of obtaining the quantitative index D", of the degree of damages of the beam structure are supports of two end spans located at both ends of the continuous beam, and a measurement point is arranged at each of the two supports of the end spans of the continuous beam to identify single-damage conditions and multi-damage conditions of the beam structure.