CN111912589A - Method for identifying beam structure damage degree based on deflection influence line change quantity - Google Patents

Method for identifying beam structure damage degree based on deflection influence line change quantity Download PDF

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CN111912589A
CN111912589A CN202010548185.5A CN202010548185A CN111912589A CN 111912589 A CN111912589 A CN 111912589A CN 202010548185 A CN202010548185 A CN 202010548185A CN 111912589 A CN111912589 A CN 111912589A
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damage
influence line
change
representing
change quantity
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CN111912589B (en
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陈志为
张健
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Xiamen University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0041—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress
    • G01M5/005—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress by means of external apparatus, e.g. test benches or portable test systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G01N3/14—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces generated by dead weight, e.g. pendulum; generated by springs tension
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0001—Type of application of the stress
    • G01N2203/0003—Steady
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/003—Generation of the force
    • G01N2203/0032—Generation of the force using mechanical means
    • G01N2203/0033—Weight
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075—Strain-stress relations or elastic constants
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/067—Parameter measured for estimating the property
    • G01N2203/0682—Spatial dimension, e.g. length, area, angle

Abstract

A method for identifying the damage degree of a beam structure based on the deflection influence line change amount comprises the following steps: 1) representing the influence line change quantity fitting curve by using a piecewise quadratic function, 2) identifying the influence line change quantity fitting curve based on a sparse regularization method, and 3) carrying out damage quantification on the beam structure according to the influence line change quantity fitting curve. The invention provides a method for changing and estimating the bending stiffness change quantity based on a deflection influence line so as to realize damage degree identification. And determining an influence line change curve from the actually measured influence line change quantity with noise by piecewise quadratic function fitting, and simplifying the problem into the identification of the change quantity of the quadratic term coefficients of a plurality of piecewise functions. By introducing the sparse regularization method, matrix ill-condition of the inverse problem identification equation is improved, and good robustness of identification can be ensured. The method does not need to establish a finite element model, has definite physical significance for damage indexes, and has the advantages of sensitivity to local damage and good noise immunity.

Description

Method for identifying beam structure damage degree based on deflection influence line change quantity
Technical Field
The invention relates to the field of engineering structure health monitoring, in particular to a method for identifying the damage degree of a beam structure based on deflection influence line change.
Background
An ideal method for identifying the damage of structure features that the damage index which can reflect the inherent characteristics of structure and is sensitive to damage is used to judge the damage of structure, the position and degree of damage and the residual service life of structure. The influence line is the inherent characteristic of the bridge structure, has definite physical significance, has good sensitivity to structural damage, and is suitable for developing a key index for evaluating the state of the bridge. As the structural performance of the bridge deteriorates during service, the influence line changes in an adverse direction. By monitoring the influence line states and the change trends of the bridge in different use stages, the method is beneficial to finding out the local early damage of the bridge, and has important significance for guaranteeing the safety of the bridge in the operation period.
At present, some scholars abroad apply bridge influence lines to structural damage identification. For example, Choi and the like research an elastic damage load mechanism based on a static displacement change caused by damage, and realize the damage positioning and quantification of a static beam based on the change of a displacement influence line. Zaurin utilizes video streaming technology to identify bridge influence lines and identifies damage by Mahalanobis distance construction indexes. The Kowna proposes that the deflection influence line and the first-order and second-order derivatives thereof are utilized to carry out damage identification, and the influence of the load moving speed on the identification effect is analyzed. The method has the advantages that the deflection influence line of the span-middle position of the variable-section beam is deduced by Xuyonghua, and the feasibility of the deflection influence line change quantity and the derivative indexes thereof for identifying the damage of the variable-section beam bridge is verified. The method for identifying the damage based on the variable quantity of the influence line of the front corner and the rear corner of the damaged simply supported beam bridge and the curvature of the difference value is provided in the Yangtze festival. Chen utilizes the structural health monitoring system to identify the stress influence line of the hong Kong Qingma bridge, and verifies the influence line index to identify the effectiveness of local damage of the long-span suspension bridge.
Recently, there has been proposed a method for determining the degree of damage of a beam structure using an influence line. For example, Chen derives an explicit relationship between deflection-influence line changes and structural damage, and then proposes a damage quantification method based on deflection-influence line changes. The method has the disadvantage that precise finite element model assistance is required, which adds considerable difficulty and additional error to practical application. Zeinail and Story propose to estimate bending stiffness based on a second derivative of a deflection influence line and determine the damage degree according to the structural damage index. The method does not need to establish a finite element model, and the damage index has definite physical significance. In order to reduce the adverse effect of noise in the influence line on identifying the bending stiffness of the cross section, Zeinail and Story further propose fitting a deflection influence line curve based on an iterative multi-parameter gihonov regularization (IMTR) method. By curve fitting the measured influence lines, the method is not too sensitive to noise interference. However, considering that the influence line change of the beam caused by early damage is far smaller than the influence line itself, the noise resistance of the method is enhanced by the curve fitting of the influence line, and simultaneously, the influence line change component containing damage information is possibly removed in a large amount, so that the sensitivity of the influence line change component to the damage is reduced.
According to the characteristic that the deflection influence line changes and directly reflects the structural damage, the method proposes that the bending rigidity change amount is estimated through the change of the influence line so as to identify the damage degree. The amount of change in the influence line caused by the damage is typically an inverse problem to find out the actual damage location and damage level from many possibilities. Inverse problem identification equations are usually ill-conditioned, and regularization methods are often used to improve the solution of ill-conditioned equations, thereby ensuring good robustness of the identification solution. An optimization objective function can be established through a regularization method, and an optimal coefficient vector is determined from the optimization objective function, so that the estimated influence line change amount is closest to actual measurement. In recent years, sparse regularization methods have been used to deal with the ill-posed problems of damage identification, load identification, and data repair, among others. The method solves for sparsity, i.e., the solution has mostly zero (or approximately zero) sequence in the spatial domain, or the solution has a sparse representation under an orthogonal basis or framework in the spatial domain.
Disclosure of Invention
The invention mainly aims to provide a method for identifying the damage degree of a beam structure based on deflection influence line change, which can estimate the bending rigidity change based on deflection influence line change, further provides a damage degree identification method, introduces a sparse regularization method to identify influence lines and change a fitting curve, and improves the solution of an ill-conditioned equation of an inverse problem.
The invention adopts the following technical scheme:
a method for identifying the damage degree of a beam structure based on the deflection influence line change amount is characterized by comprising the following steps: 1) representing an influence line change quantity fitting curve by using a piecewise quadratic function; 2) identifying a fitting curve of the influence line change quantity based on a sparse regularization method; 3) and carrying out damage quantification on the beam structure according to the fitted curve of the influence line change quantity.
Preferably, the piecewise quadratic function is Δ ΦfΩ Δ a, where Δ ΦfRepresenting the amount of change of the fit influence line, Δ Φf＝Φf,d-Φf,u，Φf,uAnd phif,dRespectively are the fitting influence lines before and after the damage; Δ a represents a quadratic coefficient change amount Δ a ═ ad-au，auAnd adAre the quadratic term coefficient vectors before and after the damage, respectively, and omega is the fitting matrix.
Preferably, the step 2) specifically includes the following steps:
the measured influence line change quantity and the fitting influence line change quantity have the following relation: delta phim＝ΔΦf+η；ΔΦmRepresenting the actually measured influence line change quantity, and representing the fitting residual error by eta; will be delta phifSubstituting for Ω Δ a, the fit residual is: eta is delta phim- Ω Δ a; by means of1The norm is a regular term, and an optimization objective function is established as follows:
Figure BDA0002541505970000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002541505970000022
a set of variables to be solved deltaa representing the minimization of the objective function,
Figure BDA0002541505970000023
which represents the sum of the squares of the fitted residuals,
Figure BDA0002541505970000024
representing a regularization term, and λ representing a regularization parameter;
determining quadratic terms by optimization of an optimization objective functionAfter the coefficient is changed by Δ a, substituted into Δ ΦfA fitted curve that affects the amount of line change is constructed.
Preferably, in step 3), by
Figure BDA0002541505970000031
Calculating the change of the flexibility of the simply supported beam caused by the damage, wherein delta phi' (x) ═ phi ″, the change of the flexibility of the simply supported beam caused by the damage is calculatedd(x)-Φ″u(x)，Φ″uAnd phi ″)dSecond derivative of the curve fitted to the deflection influence line, m, representing the lossless and the damaged state, respectivelyu(x) Representing the bending moment per unit vertical force acting on that particular point causing the x position.
Preferably, in step 3), by
Figure BDA0002541505970000032
Calculating the change of the compliance of the continuous beam, Delta phisIs the component of the variation caused by the variation of the reaction force of the support.
Preferably, in step 3), if the cross-sectional initial bending stiffness EI is knownuThen the section bending stiffness of the damaged beam can be determined:
Figure BDA0002541505970000033
if the relative change of the bending rigidity of the section is used for representing the damage degree of the x position, a damage quantitative index is defined:
Figure BDA0002541505970000034
wherein Δ F (x) is the change in beam cross-section compliance, EIuAnd EIdRepresents the flexural rigidity in the intact and damaged state, and Δ EI is the change in the cross-sectional flexural rigidity.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
1. the invention provides a method for changing and estimating the bending stiffness change quantity based on a deflection influence line so as to realize damage degree identification. And determining an influence line change curve from the actually measured influence line change quantity with noise by piecewise quadratic function fitting, and simplifying the problem into the identification of the change quantity of the quadratic term coefficients of a plurality of piecewise functions. By introducing the sparse regularization method, matrix ill-condition of the inverse problem identification equation is improved, and good robustness of identification can be ensured. The method does not need to establish a finite element model, has definite physical significance for damage indexes, and has the advantages of sensitivity to local damage and good noise immunity.
2. Compared with the existing damage indexes, the damage index based on the influence line change quantity is more sensitive to the local damage of the bridge and is insensitive to the change of environmental factors, so that the method is more suitable for detecting the local damage of the bridge in the operating environment.
3. According to the method, the early damage of the structure is considered to only occur locally, and the damage coefficient to be solved has obvious sparsity. A sparse regularization method is introduced for solving, small local damage and large noise interference are considered, and good robustness of an identification solution can be still ensured.
Drawings
FIG. 1 is a schematic view of a simply supported beam;
FIG. 2 is a deflection influence line before and after a single injury;
FIG. 3. deflection influence line change for a single lesion;
FIG. 4. Damage level identification based on a single influence line: a first damage working condition;
FIG. 5. Damage level identification based on multiple influence lines: a first damage working condition;
FIG. 6. deflection influence lines before and after multiple damages;
FIG. 7. deflection before and after multiple lesions affects the line;
FIG. 8. Damage level identification based on multiple influence lines: a second damage condition;
FIG. 9 is a schematic view of a continuous beam;
FIG. 10. Damage level identification based on multiple influence lines: a continuous beam damage condition;
FIG. 11 is a schematic diagram of a simple aluminum beam for a laboratory;
FIG. 12 is a schematic diagram of a laboratory beam at the stage of injury;
FIG. 13. model update output response versus measured response;
FIG. 14. deflection influence line changes at different locations: a first damage condition of a laboratory;
FIG. 15. Damage level identification based on a single influence line: a first damage condition of a laboratory;
fig. 16. damage degree recognition result based on a plurality of influence lines: a first damage condition of a laboratory;
FIG. 17. Damage level identification based on different number of influence lines: a second damage condition of the laboratory;
FIG. 18 shows the results of the identification of the degree of damage;
FIG. 19 is a schematic diagram and a physical diagram of a simple aluminum beam in a laboratory;
FIG. 20 is a diagram of a laboratory beam at the stage of injury;
FIG. 21 is a comparison of the influence line changes of different measuring points under a single damage condition;
FIG. 22 is a graph showing the comparison of the variation of the influence lines of different measuring points under two damage conditions;
FIG. 23 shows the results of the recognition of the damage degree at different measuring point positions under a single damage condition;
FIG. 24 shows the results of the recognition of the damage degree at different measuring point positions under two damage conditions;
the invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
The invention provides a method for identifying the damage degree of a beam structure based on deflection influence line change, which mainly comprises the following steps:
and step S1, representing an influence line change quantity fitting curve by using a segmented quadratic function.
The actual change amount of the influence line cannot be obtained generally, and a feasible method is to actually measure the deflection influence line before and after the damage, so as to estimate the change amount of the influence line. However, the actual measurement influence line is inevitably interfered by noise such as measurement errors, and the second derivative of the actual measurement influence line can further amplify the noise component, so that the noise component is used for damage identification, and the effect is greatly reduced or even completely failed. An influence line change curve can thus be fitted from the noisy measured influence line changes and used for damage level identification.
Determining a suitable influence line fitting function is a problem that needs to be solved first. Considering that the deflection influence lines of the front beam and the rear beam after damage can be kept smooth and continuous basically, the influence line function to be fitted should also meet the characteristics of continuity and smoothness. In addition, if the beam is divided evenly into several sections and sufficiently finely, the bending rigidity and the bending moment of the section at the center section of each section can be taken as representative values of the section, and the values are constants. The second derivative of the influence line piecewise curve derived from equation (1) is constant, so the second derivative of the influence line function to be fitted should also be constant. The above factors are comprehensively considered, and the following piecewise quadratic function fitting influence line is adopted:
Figure BDA0002541505970000051
in the formula phii(x) Is a quadratic function of the i-th fitting influence line, ai,bi,ciAnd coefficients of a quadratic term, a primary term and a constant term of the ith segment of function are respectively expressed, i is more than or equal to 1 and less than or equal to Ns, and Ns represents the number of segments.
Introducing a fitting matrix omega, and a piecewise quadratic function fitting expression of the influence line can be expressed as:
Φf＝Ωa
in the formula, the coefficient vector of quadratic term a ═ a1,a2,…aN}T. For a given beam structure, the matrix Ω before and after damage can remain unchanged. Different quadratic term coefficients are adopted, and influence line fitting curves before and after damage can be respectively constructed:
Φf,u＝Ωau
Φf,d＝Ωad
wherein phif,uAnd phif,dBefore and after injury, respectivelyThe fitting influence line of (a)uAnd adThe quadratic term coefficient vectors before and after the injury, respectively.
As can be derived from the above equation, the influence line change can be expressed as a function of the change in the coefficients of the piecewise quadratic term:
ΔΦf＝ΩΔa
wherein Δ ΦfRepresents the amount of change in the fit influence line:
ΔΦf＝Φf,d-Φf,u
Δ a represents the amount of change in the coefficient of the quadratic term:
Δa＝ad-au
and step S2, identifying a fitting curve influencing the line change quantity based on a sparse regularization method.
Fitting an influence line change curve from the actually measured influence line change amount with noise, wherein the actually measured influence line change amount and the fitted influence line change amount have the following relation:
ΔΦm＝ΔΦf+η
in the formula, Δ ΦmRepresenting the amount of change, Δ Φ, of the measured influence linefRepresents the amount of change in the fit influence line, and η represents the fit residual. Finding the optimal solution from a plurality of possible influence line fitting solutions based on the actually measured influence lines is a typical inverse problem. Due to the fact that fitting residual errors caused by noise interference exist, the inverse problem identification equation is ill-conditioned, and a regularization method needs to be introduced to improve the solution of the problem.
From step S1, it can be known that the influence line change curve to be fitted can be represented as a function of the change amount of the segmented quadratic coefficient, so that the optimal recognition problem of the influence line fitting solution can be converted into a problem of recognizing the change amount of the quadratic coefficient. Will be delta phifSubstituting Δ Φ into Ω Δ am＝ΔΦf+ η, then the fit residual can be rewritten as:
η＝ΔΦm-ΩΔa
and segmenting the beam to be recognized into enough subareas, and taking the secondary term coefficient change quantity of all the subareas as the quantity to be recognized. It is derived that the change of the section flexibility is related to the influence line change second-order linearity, and has a clear corresponding relation with the change of the quadratic term coefficient of the piecewise function. That is, if the section compliance changes, the quadratic coefficient will change accordingly, and vice versa. Considering that the early damage of the structure occurs only locally, only the cross-sectional compliance of the individual sub-regions changes. Correspondingly, the coefficient variation of the quadratic term is not zero at a few damaged positions, and other positions are zero (or nearly zero), so that the sparsity is obvious.
Finding the optimal solution from a plurality of possible influence line fitting solutions based on the actually measured influence lines is a typical inverse problem. Due to the fact that fitting residual errors caused by noise interference exist, the inverse problem identification equation is ill-conditioned, and a regularization method needs to be introduced to improve the solution of the problem. The sparse regularization method can accurately solve sparse solutions. Therefore, a sparse regularization method is introduced for identifying the influence line change curve, with l1The norm is a regular term, and an optimization objective function is established as follows:
Figure BDA0002541505970000071
in the formula (I), the compound is shown in the specification,
Figure BDA0002541505970000072
a set of variables to be solved deltaa representing the minimization of the objective function,
Figure BDA0002541505970000073
which represents the sum of the squares of the fitted residuals,
Figure BDA0002541505970000074
a regularization term is represented and λ represents a regularization parameter.
After the quadratic term coefficient change quantity delta a is determined by the optimization solution of the formula, the quadratic term coefficient change quantity delta a is substituted into delta phifA fitted curve can be constructed that affects the amount of line change.
Step S3, carrying out damage quantification of the beam structure according to the fitted curve of the deflection influence line change quantity
The relationship between the second derivative of the beam deflection influence line and the section bending rigidity is as follows:
Figure BDA0002541505970000075
wherein EI (x) represents the bending rigidity of the cross section at the x position, phi' (x) represents the second derivative of the deflection influence line x position of a specific measuring point, and m (x) represents the bending moment of the x position caused by the unit vertical force acting on the specific measuring point.
Assuming that the beam is locally damaged and causes a change in cross-sectional bending stiffness Δ EI:
Figure BDA0002541505970000076
wherein the subscripts u and d represent the non-destructive and destructive states, EI, respectivelyuAnd EIdFlexural rigidity, m, representing the state of intact and damageduAnd mdRepresenting bending moments in undamaged and damaged states. PhiuAnd phi ″)dThe second derivative of the deflection influence line representing the damage-free and damage states. In incremental form, the above formula can be rewritten as:
Figure BDA0002541505970000077
Δm(x)＝md(x)-mu(x)
ΔΦ″(x)＝Φd″(x)-Φu″(x)
when the sectional compliance is expressed by the reciprocal of the sectional bending stiffness, the change Δ F of the sectional compliance due to damage is:
Figure BDA0002541505970000078
for a simply supported beam structure, the beam section rigidity is reduced to change a deflection influence line by delta phi, the bending moment before and after damage is kept unchanged by delta m as 0, and the substitution of the formula has the following steps:
Figure BDA0002541505970000081
for a multi-span continuous beam structure, the reduction of the rigidity of the cross section of a damaged span can change the counterforce of the support, further cause the change of the bending moment of the cross section and transmit the change of the influence line to the non-damaged span. Therefore, the change of the influence line of the deflection of the continuous beam should include two components, and the change component Δ Φ directly caused by the decrease of the bending rigiditybVariation component Delta phi caused by variation of support reaction forcesThen, there are:
ΔΦ(x)＝ΔΦb(x)+ΔΦs(x)
the influence line change quantity delta phi used for identifying the bending stiffness of the section of the continuous beam is eliminated by analyzing the beam bending stiffness estimation principlesComposition and not taking into account changes in section bending moment caused by changes in abutment reaction forces. Substituting the delta F to solve the expression can obtain the following section flexibility change quantity of the multi-span continuous beam:
Figure BDA0002541505970000082
according to the formula, the change quantity of the influence line of the deflection of the continuous beam caused by the change of the counter force of the support is identified and eliminated. Taking the middle support counterforce of a two-span continuous beam as an example, the support counterforce of a nondestructive and damaged beam under the action of unit force of movement is assumed to be Ps,u(x) And Ps,d(x) Change of reaction force of support Δ Ps(x)＝Ps,d(x)-Ps,u(x) In that respect By the mutual theorem of the reaction force, the deflection influence line change quantity caused by the change of the support reaction force can be obtained:
ΔΦs(x)＝ΔPs(x)·Δ1p
in the formula,. DELTA.1pAnd the unit force is expressed to act on the measuring point position of the equivalent simply supported beam to cause the deflection of the original middle support.
By utilizing the virtual work principle, virtual unit force is acted on the original middle support to generate virtual displacement
Figure BDA0002541505970000083
The deformation coordination equation of the damaged beam can be established:
Figure BDA0002541505970000084
substituting the above formula into delta phis(x)＝ΔPs(x)·Δ1pThe following can be obtained:
Figure BDA0002541505970000085
the continuous beam is divided into cells, assuming that a local early damage causes a decrease in stiffness of some or few cells. Suppose the central position of the injury unit is x0The length of the damage is 2, i.e. the damage interval is [ x ]0-,x0+]Then, then
Figure BDA0002541505970000086
Can be expressed as:
Figure BDA0002541505970000087
since the damaged cell length is much smaller than the beam length (< L), the numerical value of the second term of the above equation is much smaller than the first term, then:
Figure BDA0002541505970000091
if the section initial bending rigidity EIuIt is known that the above formula can be used to obtain
Figure BDA0002541505970000092
And further the deflection influence line change caused by the change of the counter force of the support can be obtained.
Through the derivation, a display relation of the second derivative influencing the change of the influence line and the change of the section flexibility is established, and
Figure BDA0002541505970000093
and
Figure BDA0002541505970000094
and respectively calculating the flexibility change of the simple beam and the continuous beam caused by the damage. Given the known initial bending stiffness EI of the cross sectionuThen the section bending stiffness of the damaged beam can be determined:
Figure BDA0002541505970000095
if the relative change in cross-sectional bending stiffness is used to represent the degree of x-site damage, a damage quantification index can be defined:
Figure BDA0002541505970000096
examples of applications are:
example 1: numerical model damage quantification for simply supported beams and continuous beams
The design size of the simply supported beam model is shown in fig. 1, the span L is 10m, the height h of the rectangular cross section is 1m, the width b is 0.5m, and the elastic modulus E is 3.25 × 1010N/m2. MATLAB programming software adopts plane beam units to establish a finite element model, 100 beam units are evenly divided along the longitudinal direction of the beam, and the length of each unit is 0.1 m. And (3) sequentially applying unit force (F is 1000N) to the beam unit nodes, outputting deflection of a mid-span position (x is 5m), and further acquiring a beam mid-span deflection influence line in a lossless state. Simulating that the simply supported beam has certain damage in the 5 m-6 m beam section interval, and assuming that the bending rigidity is reduced by 25 percent, namely EId＝0.75EIu. The same moving unit force load is applied by the same method, and the influence line of the deflection of the middle span of the lower beam in the damaged state can be obtained.
In order to simulate the measured influence line, 1% of random white noise was considered in the numerical simulation. Combining the piecewise quadratic function representation and the simply supported beam boundary conditions, a fitting matrix omega can be obtained, the quadratic coefficient change quantity delta a can be identified through sparse regularization, the influence line change quantity can be further identified, and finally, a fitting curve of the beam mid-span deflection influence line change quantity can be determined as shown in fig. 2. Based on the influence line change quantity fitting curve obtained by identification, the flexibility change quantity at the corresponding position of each section of the whole beam can be obtained as shown in fig. 3, and the information reflected in the graph shows that the method has good evaluation effect on the damage degree of the whole beam, the identification error of the damage degree of the lossless region is basically negligible, and the two damage regions are relatively consistent. Taking every ten units of the whole beam as a section, quantitatively analyzing the damage degree of each section by using the damage evaluation index of the relative change amount beta of rigidity, and referring to fig. 4 as a damage degree identification result, it can be seen that the method can accurately describe the damage degree of the inner beam of each section, the damage degree identification result of the damaged section is 23.5%, the difference between the damage degree identification result and the actual damage degree 25% is only 1.5%, and the damaged area is effectively quantified. In addition, the peripheral sections of the damaged area, such as two lossless areas of 4m to 5m and 6m to 7m, have some misjudgment, but are not higher than 5%, and can be basically ignored.
In order to test the influence of different noise levels on the identification result of the damage degree of the simply supported beam, 1%, 3% and 5% of noise interference is respectively applied to the reference influence lines before and after the damage. The damage degree identification is performed by using the influence line change amounts under different noise levels, and as shown in fig. 5, for example, the identification result pair shows that, as the noise level increases, the relative error between the damage degree identification result and the actual damage degree is larger, and the erroneous judgment of the lossless region is more easily caused. Overall, under a certain noise level, the damage identification result obtained by the method is more accurate and reliable, and the method has stronger robustness to noise.
In order to test the influence of the multi-damage working condition on the identification result of the damage degree of the simply supported beam, one simply supported beam with two damages is selected for analysis, and the specific material parameters of the simply supported beam are the same as those of the simply supported beam. The damage position interval is 2 m-3 m, 7 m-8 m, the bending rigidity of the unit is respectively attenuated by about 15 percent and 25 percent, namely
Figure BDA0002541505970000101
The sensor measuring point is arranged at the span 1/2 (x ═ 5 m). In the numerical simulation analysis process, the influence of 3% random noise is considered, and as shown in fig. 6, it can be found that it is difficult to directly judge the damage region from the actually measured influence line change amount under two damage conditions. In addition, compared with the single damage condition, the real influence line change amount under the two damage conditions is in a step shape, the damaged area is positioned at the periphery of the left and right vertex angle areas, and meanwhile, the influence line change amount of the damaged area and the undamaged area is not obviously different as that under the single damage condition, so that the damage evaluation effect is obviously influenced to a certain degree. Fig. 7 is a comparison graph of the change amount of compliance, and it can be seen from the graph that the two are substantially identical in curve form, and besides there is a misjudgment with a small damage degree identification result at positions from 7m to 8m, the error of the rest area is substantially negligible. As shown in fig. 8, when the damage identification result is further analyzed by using the damage evaluation index, i.e., the relative change amount of stiffness, it can be observed that although a certain error exists with respect to the true value, the error of the method does not exceed 5% in the damaged area and the undamaged area, and the method can generally perform positioning and quantification on two damages of 2m to 3m and 7m to 8 m.
The design size of the continuous beam model is shown in fig. 9, the span L is 10m, the height h of the rectangular cross section is 1m, the width b is 0.5m, and the elastic modulus E is 3.25 × 1010N/m2. MATLAB programming software adopts a plane beam unit for modeling, 200 beam units are evenly divided along the longitudinal direction of the beam, and the length of each unit is 0.1 m. Unit force (F is 1000N) is sequentially applied to the beam unit nodes, deflection of a span position (x is 5m) of the span center 1/4 is output, and then deflection influence lines in a nondestructive state are obtained. Simulating that the continuous beam has certain damage in the beam section interval of 7-8 m, and assuming that the bending rigidity is reduced by 25 percent, namely EId＝0.75EIu. By applying the same moving unit force load in the same way, the deflection influence line of 1/4 span in the beam span under the damaged state can be obtained.
First, as shown in fig. 10, the reaction force influence lines of the continuous beam support in the non-damaged state and the damaged state are output, respectively, and it can be found that the reaction force influence lines of the support reach a peak value at the mid-span support position and gradually decrease to zero away from the mid-span support position. Meanwhile, the two curve tracks before and after the injury are relatively close, and no obvious difference exists. Subsequently, the change amount of the influence line of the seat reaction force before and after the damage is calculated as shown in fig. 11, and it is found from the lower graph that the peak position of the curve of the change amount of the seat reaction force corresponds to the damaged region, and the seat reaction force in the vicinity of the damaged region is changed to a large extent. Further calculation of the amount of change in the influence line caused by the change in the reaction force of the carrier is shown in fig. 12, and it can be seen that the change in the influence line caused by the change in the reaction force of the carrier has a curve form similar to the influence line of the reaction force of the carrier
3% random white noise was considered in the numerical simulation. Firstly, a fitting matrix Ω' can be obtained by combining the piecewise quadratic function representation and the continuous beam boundary condition, and the quadratic coefficient change amount Δ a can be identified through sparse regularization so as to identify the influence line change amount, and finally, the deflection influence line change amount fitting curve at the crossing of the beam 1/4 can be determined as shown in fig. 13. And the identification result of the influence line change quantity fitting curve is matched with the real influence line change quantity, which shows that the method has good fitting effect. Based on the influence line change quantity fitting curve obtained by identification, the flexibility change quantity at the corresponding position of each section of the whole beam can be obtained as shown in fig. 14, and the identification results of the method on both the damaged area and the lossless area are closer to the real state from the information reflected in the figure. Fig. 15 shows a damage degree identification result, and it can be found that the method can more accurately describe the damage degree of the inner beam of each section, the damage degree identification result of the damaged section is 24.3%, which is different from the actual damage degree by 25% by only 0.7%, and the damaged area is effectively quantified. In addition, the peripheral sections of the damaged area, for example, two lossless areas of 6m to 7m and 8m to 9m, have some misjudgment, but are not higher than 5%, and can be basically ignored.
In order to test the influence of the multi-damage working condition on the continuous beam damage degree identification result, one continuous beam with two damages is selected for analysis, and the specific material parameters of the continuous beam are the same as those of the simply supported beam. The damage position interval is 3 m-4 m, and 14 m-15 m, the bending rigidity is reduced by about 25% and 15%, respectively, namely
Figure BDA0002541505970000111
The sensor measuring point is arranged at the span 1/4 (x ═ 5 m). In the analysis process, the influence of 3% random noise is considered, as shown in fig. 16, and as compared with the case of a single damage, there are two more significant corners in the change amount of the influence line under two damage conditions, and the two corners correspond to the damaged area. Similarly, under two working conditions, the damaged area is difficult to be positioned through actually measured influence line change quantity. The results of the flexibility index change amount and the damage degree obtained by identifying the influence line change amount caused by the reduction of the section rigidity are respectively shown in fig. 17 and 18, and the damage quantification method has a good effect of identifying two damages of the continuous beam by combining the results of the two graphs. The flexibility change index curve can be basically identical with the real value curve, and the quantification of the damage of a plurality of places of the continuous beam is realized. From fig. 18, the method has a slight error in the identification result of the local lossless region around the damaged region, and the error of the remaining lossless region is substantially negligible. For the damaged area, the recognition result of the first damage degree is 27.4%, the recognition result of the second damage degree is 11.1%, and the relative error with the true value is controlled within 5%.
Example 2: laboratory simply supported aluminum beam damage quantification
The simple-supported aluminum beam has a box-shaped cross section, a length of 3.16m, a height of 0.025m and a width of 0.15m, and is schematically shown in FIG. 19. Its elastic modulus E is 6.9X 1010N/m2The mass block of 2.47Kg is used for static loading at a certain interval (the unit interval divided by the model), thereby simulating the motionDynamic vertical unit force. Displacement meters are arranged at part of the critical section positions (1/4 span, 1/2 span and 3/4 span) of the beam, wherein the sampling frequency is 50 Hz.
In order to simulate the damage and carry out positioning and quantification on the damage, the whole beam is divided into 32 areas, and the area ranges of the head unit and the tail unit are 8cm, and the area ranges of the other units are 10 cm.
The damage condition simulated in the laboratory mainly comprises the following two conditions:
(1) single damage condition
(a) In the lossy stage experiment, an opening is cut at a position (area No. 23) of 2.205-2.225 m from the left end of the beam to simulate unit damage, and the inertia moment of the opening is reduced by 55% (see figure 20 in detail, and (a) is a single damage working condition).
(2) Two damage conditions
A second port was then cut near the span of the beam 1/4 to reduce its moment of inertia by 30% to simulate a second injury (see in detail fig. 20(b) for two injury conditions, (c) for a phase of injury laboratory beam illustration).
First, in order to obtain the reference influence line, a load is applied by a static load method in an experiment under a lossless state, and the response data of the displacement meter of the 3 positions is output, so that the reference deflection influence line corresponding to each position is obtained. And then cutting off the hole to simulate the damage working condition, and recording and outputting the deflection influence line at the corresponding position in the damage state. Fig. 21 and 22 show the change amount of the deflection influence line under different damage conditions. From fig. 21, it can be found that although there is noise interference under a single damage condition, the influence line change amount of each measuring point can still better locate the damage position, and the deflection influence line change amount at the 3/4 cross measuring point closest to the damage position is most significant, and then 3/4 span and 1/4 span are followed. Further observing fig. 22, it can be found that the measuring points of each sensor under the two damage conditions can also describe the positions of the two damages to a certain extent, and meanwhile, due to the existence of the two damages, the difference of the change amount of the influence lines of the sensors at the measuring points is not significant.
The damage position and the damage degree are identified by the method described in this chapter based on the above-mentioned actually measured change amount of the influence line before and after damage, and the result is shown in fig. 23: obviously, the damage unit can be located, and the recognition effect of the damage degree varies with the distance between the displacement meter and the damage position, and the closer the distance is, the better the effect is. Since the 1/4 transposition displacement meter information is relatively low in signal-to-noise ratio with respect to other sensor information, which is relatively distant from the damage position, the error of the degree of damage recognized by the information is also largest. In addition, the damage identification result of the damage area at the periphery of the damaged area still has some errors compared with the damage identification result of other positions. The reason is that the nodes on both sides of the damaged unit are shared by the peripheral lossless units and the damaged unit, so that the nodes are influenced by the two units; in addition, the damage degree identification effect of the sparse regularization method also has the phenomenon that the damaged area transits to the lossless area, so that the unit of the transitional area has some damage misjudgment.
Similar to a single damage working condition, the method is used for carrying out damage identification on two damage working conditions. Fig. 24 shows the recognition results of two lesions. It can be seen that, through the method, the damaged units No. 10 and No. 23 can be well positioned by utilizing the information of each position displacement meter, and similar to the problem reflected by single damage, the peripheral units of the damaged units are also misjudged to a certain extent. In addition, the damage identification effects of different position displacement meters are different, the damage identification effect of 1/4 cross position displacement meters is poor, the identification effect of 1/2 cross position displacement meters is good, and the identification error of the 1/2 cross position displacement meters at two damage units is not higher than 5%. Therefore, the experimental result basically accords with the conclusion of numerical simulation, that is, the damage identification method based on the influence line change quantity not only can accurately realize damage positioning, but also has good damage quantification effect.
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.

Claims (6)

1. A method for identifying the damage degree of a beam structure based on the deflection influence line change amount is characterized by comprising the following steps: 1) representing an influence line change quantity fitting curve by using a piecewise quadratic function; 2) identifying a fitting curve of the influence line change quantity based on a sparse regularization method; 3) and carrying out damage quantification on the beam structure according to the fitted curve of the influence line change quantity.
2. The method for identifying the degree of damage of a beam structure based on the amount of change in the deflection influence line as set forth in claim 1, wherein: the piecewise quadratic function is Δ ΦfΩ Δ a, where Δ ΦfRepresenting the amount of change of the fit influence line, Δ Φf＝Φf,d-Φf,u，Φf,uAnd phif,dRespectively are the fitting influence lines before and after the damage; Δ a represents a quadratic coefficient change amount Δ a ═ ad-au，auAnd adAre the quadratic term coefficient vectors before and after the damage, respectively, and omega is the fitting matrix.
3. The method for identifying the degree of damage of a beam structure based on the amount of change in the deflection influence line as set forth in claim 1, wherein: the step 2) specifically comprises the following steps:
the measured influence line change quantity and the fitting influence line change quantity have the following relation: delta phim＝ΔΦf+η；ΔΦmRepresenting the actually measured influence line change quantity, and representing the fitting residual error by eta; will be delta phifSubstituting for Ω Δ a, the fit residual is: eta is delta phim- Ω Δ a; by means of1The norm is a regular term, and an optimization objective function is established as follows:
Figure FDA0002541505960000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002541505960000012
a set of variables to be solved deltaa representing the minimization of the objective function,
Figure FDA0002541505960000013
which represents the sum of the squares of the fitted residuals,
Figure FDA0002541505960000014
representing a regularization term, and λ representing a regularization parameter;
after the quadratic term coefficient change quantity delta a is determined by the optimization of the optimization objective function, the quadratic term coefficient change quantity delta a is substituted into delta phifA fitted curve that affects the amount of line change is constructed.
4. The method for identifying the degree of damage of a beam structure based on the amount of change in the deflection influence line as set forth in claim 1, wherein: in step 3), by
Figure FDA0002541505960000015
Calculating the change of the flexibility of the simply supported beam caused by the damage, wherein delta phi' (x) ═ phi ″, the change of the flexibility of the simply supported beam caused by the damage is calculatedd(x)-Φ″u(x)，Φ″uAnd phi ″)dSecond derivative of the curve fitted to the deflection influence line, m, representing the lossless and the damaged state, respectivelyu(x) Representing the bending moment per unit vertical force acting on that particular point causing the x position.
5. The method for identifying the degree of damage of a beam structure based on the amount of change in the deflection influence line as set forth in claim 1, wherein: in step 3), by
Figure FDA0002541505960000016
Calculating the change of the compliance of the continuous beam, Delta phisIs the component of the variation caused by the variation of the reaction force of the support.
6. The method for identifying the degree of damage of a beam structure based on the amount of change in the deflection influence line as set forth in claim 1, wherein: in step 3), if the initial bending rigidity EI of the section is knownuThen the section bending stiffness of the damaged beam can be determined:
Figure FDA0002541505960000021
if the relative change of the bending rigidity of the section is used for representing the damage degree of the x position, a damage quantitative index is defined:
Figure FDA0002541505960000022
wherein Δ F (x) is the change in beam cross-section compliance, EIuAnd EIdRepresents the flexural rigidity in the intact and damaged state, and Δ EI is the change in the cross-sectional flexural rigidity.
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