CN104517036A - Simply-supported piece damage identification method based on strain statistical moment - Google Patents
Simply-supported piece damage identification method based on strain statistical moment Download PDFInfo
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Abstract
The invention discloses a simply-supported piece damage identification method based on a strain statistical moment. The simply-supported piece damage identification method comprises the following steps: (1) uniformly distributing a plurality of strain gages on a simply-supported piece as measuring points and respectively obtaining strain statistical moment vectors of all the measuring points of the simply-supported piece under undamaged and damaged states, and determining a damaged part on the simply-supported piece by using a difference value between the strain statistical moment vectors; (2) establishing a finite element model and dividing a finite element unit; simulating a power process the same as the step (1) to obtain an analysis vector formed by the strain statistical moments of all nodes under a simulated state; and (3) carrying out model revising by using a least square method according to a damaged part positioned by the step (1) to obtain a damage degree of the potential damage finite element model. The advantages that the strain statistical moment is sensitive to partial damages and also has a good anti-noise capability are utilized so that the change of the simply-supported piece before and after damages can be directly used for positioning the structure damages; the good anti-noise capability of the strain statistical moment can be used for effectively improving the damage degree identification precision.
Description
Technical field
The invention belongs to civil engineering works structure health monitoring and damage identification technique field, more specifically, relate to a kind of freely-supported part damnification recognition method based on strain statistical moment.
Background technology
Civil engineering structure, comprises bridge, covil construction, and industrial premises etc., be often directly connected to public property safety.Structure from build in military service process, under the effect of wind load, earthquake load, artificial impact load, fatigue load and chemical corrosion, rigidity can constantly damage, produce so-called structural damage, when these damage accumulation are to certain degree, can have a negative impact to integrally-built stress performance, severe patient even causes structure ultimate failure, causes great casualties and property damage.In order to the security of the lives and property of the safe operation and user that ensure structure, civil engineer should set up the earlier damage of effective method detection architecture, sets up early warning mechanism, makes structural damage namely be found in early days in appearance, repair, avoids major accident.Therefore, monitoring structural health conditions has attracted the attention of countries in the world researcher in recent decades, and damnification recognition method determines position and quantitative judge structural damage important in inhibiting as the pith aligning of health monitoring.
The change of the structural parameters caused by structural damage often causes the change of modal parameters (comprising model frequency, Mode Shape, modal damping), and the damnification recognition method therefore based on vibration often adopts modal parameter and its other parameter derived as Damage Index.But be that it is insensitive and very responsive to measurement noises to local damage based on the greatest drawback that the damnification recognition method of mode targets exists.
In order to solve this shortcoming of the Structural Damage Identification based on modal parameter, the present invention is using the beam slab freely-supported part of flexure type as research object, the strain statistical moment of the power strain time history of direct employing structure, as Damage Index, establishes a kind of new Structural Damage Identification in conjunction with the Model Updating Technique based on least square method.Make use of the advantage of strain for local damage sensitivity on the one hand, avoid the process of model analysis in non-destructive tests, in addition on the one hand, this statistical indicator of strain statistical moment has been proved to be has good noise resisting ability, and thus the method can reduce the erroneous judgement of damage to a great extent.
Summary of the invention
For above defect or the Improvement requirement of prior art, the invention provides a kind of freely-supported part damnification recognition method based on strain statistical moment, its damage criterion adopting strain statistical moment to propose as this method, have the advantage of strain for local damage sensitivity on the one hand, as statistical indicator, there is good noise resisting ability on the other hand, make the method have extraordinary robustness; In addition, utilize strain statistical moment for the susceptibility of local damage, this method can identify structural damage degree, decreases optimized variable number to a great extent, improves precision and the efficiency of structural damage degree identification.
For achieving the above object, according to one aspect of the present invention, provide a kind of freely-supported part damnification recognition method based on strain statistical moment, comprise the following steps:
1) on freely-supported part uniform multiple foil gauge as measuring point, applying white Gaussian noise encourages, what under the harmless vector sum faulted condition that the strain statistical moment obtaining freely-supported part each measuring point under nondestructive state respectively forms, the strain statistical moment of each measuring point was formed damages vector, calculate the change vector of strain statistical moment of each measuring point before and after damage and curve plotting, according to the damage location on the mutated site determination freely-supported part of curve;
2) set up the finite element model of freely-supported part and divide finite element unit, each node of finite element unit is corresponding with the position of each measuring point on freely-supported part, simulation and step 1) identical excitation, obtain the analysis that the strain statistical moment of each node is formed under emulation mode vectorial;
3) according to step 1) damage location of locating, the stiffness coefficient arranging latent lesion finite element unit finite element model corresponding to damage location position is optimized variable, analyzing vector with two norms of the residual error damaging vector is objective function, least square method is utilized to carry out Modifying model, make two Norm minimums, obtain the degree of injury of latent lesion finite element unit, this extent of damage is the degree of injury of damage location on freely-supported part.
Preferably, step 1) in the number of measuring point of arranging be N number of, then the strain statistical moment of a kth measuring point is
Wherein
for the variance of the dynamic strain response of a kth measuring point, k≤N and
Wherein S
k(ω) be the power spectrum density of a kth measuring point, and
S
k(ω)＝ε(ω)ε
*(ω)
Wherein ε (ω) is the solution of strain vector in frequency domain of each measuring point strain composition, and
Wherein, q
ifor canonical coordinates and
for the i-th rank displacement modes of freely-supported part, F (ω) is the Fourier transform of applied force on freely-supported part, ω be force transformation to the frequency in frequency domain, k
i, m
iand c
ibe respectively the i-th rank modal stiffness, the i-th rank modal mass and the i-th rank modal damping; ψ
ifor strain mode and
wherein
for the i-th rank displacement modes of freely-supported part, l is along answering nyctitropic length variable, h
0for the thickness of freely-supported part; Therefore, the strain statistical moment M of a kth measuring point
kits i-th rank modal stiffness k
ifunction.
Preferably, described step 1) in utilize excitational equipment to encourage, described excitational equipment comprises signal generator, power amplifier and vibrator, and described excitational equipment applies the dynamic load of obeying white Gaussian noise distribution on the top of freely-supported part; Foil gauge gathers its dynamic strain response time-histories by dynamic date collecting device.
Preferably, step 3) comprise the following steps:
3.1) according to the positioning result of damage location on freely-supported part, setting is optimized variable with the stiffness coefficient of the latent lesion finite element unit of the damage location corresponding position on freely-supported part, and this optimized variable initial value is nondestructive state, and value is 1; Calculate the strain statistical moment of finite element model;
3.2) least square method is utilized to carry out Modifying model, by adjusting the stiffness coefficient α of latent lesion finite element unit on finite element model, make two Norm minimums of the residual error of the strain statistical moment of each measuring point under the strain statistical moment of each node and faulted condition;
3.3) the stiffness coefficient α of the latent lesion finite element unit identified is between 0 ~ 1, and then the degree of injury obtaining damage location on latent lesion finite element unit and freely-supported part is 1-α.
Preferably, step 3) in the finite element model of freely-supported part adopt Euler-Bernoulli beam element or rectangular plate element.
Step 3) medium power time-history analysis adopts Newmark anomalous integral Ruili damping hypothesis, calculates the displacement of measuring point, and the strain of relation computing node according to amount of deflection and strain.
In general, the above technical scheme conceived by the present invention compared with prior art, respectively the damage of freely-supported part is positioned and quantitative identification owing to utilizing strain statistical moment index and least square Model Updating Technique, improve the noise robustness of Structural Damage Identification, improve the precision of damage extent identification and the efficiency of identification, following beneficial effect can be obtained:
1) strain statistical moment both responsive to local damage, have again good noise resisting ability, the change before and after the damage of freely-supported part can be directly used in location structure damage, and the good anti-noise ability of strain statistical moment effectively can promote the precision of damage extent identification;
2) owing to first can locate the damage location on freely-supported part, damage location identifies, and decreases optimized variable during FEM updating, improves counting yield, improves the precision of structural damage degree identification.
Accompanying drawing explanation
Fig. 1 is the damnification recognition method process flow diagram that the present invention is based on strain statistical moment;
Fig. 2 is the free beam model schematic of the embodiment of the present invention;
Fig. 3 a is strain statistical moment change curve before and after operating mode the first damage of free beam for the moment;
Strain statistical moment change curve before and after the damage of free beam the second during Fig. 3 b operating mode two;
Fig. 4 a operating mode is the first damage extent identification result of free beam for the moment;
Free beam the second damage extent identification result during Fig. 4 b operating mode two;
Fig. 5 is the unidirectional simply supported slab model schematic of the embodiment of the present invention;
Strain statistical moment change curved surface before and after the first damage of simply supported slab for the moment of Fig. 6 a operating mode;
Strain statistical moment change curved surface before and after the damage of simply supported slab the second during Fig. 6 b operating mode two;
Fig. 7 a operating mode is the first damage extent identification result of simply supported slab for the moment;
Simply supported slab the second damage extent identification result during Fig. 7 b operating mode two.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.In addition, if below in described each embodiment of the present invention involved technical characteristic do not form conflict each other and just can mutually combine.
Based on a damnification recognition method for the freely-supported part of strain statistical moment, comprise following key step:
(1) white Gaussian noise excitation is applied to harmless freely-supported part, gather the dynamic strain time-histories of uniform foil gauge measuring point, and the strain statistical moment of each measuring point under calculating nondestructive state, the harmless vector of these strain statistical moments compositions; Freely-supported part in the present invention adopts free beam or simply supported slab;
(2) to there being the freely-supported part of damage to apply identical white Gaussian noise excitation, gathering the dynamic strain time-histories of uniform measuring point, and calculating the strain statistical moment under the state that damages, these strain statistical moment compositions damage vector; The freely-supported part of this step is consistent with the specification of the freely-supported part of step (1), just it has damage location;
(3) change vector curve plotting that strain statistical moment before and after the damage of freely-supported part is calculated, according to the catastrophe determination latent lesion position of curve;
(4) finite element model of freely-supported part is set up, finite element unit is divided according to the deployment scenarios of measuring point each on freely-supported part, each measuring point one_to_one corresponding on node on finite element model and freely-supported part, and the dynamic process that simulation is identical with (2), obtain the strain statistical moment under the dynamic strain time-histories of the node corresponding with each measuring point and emulation mode, these strain statistical moment composition analysis vectors.
(5) according to the positioning result of the damage location of (3), the stiffness coefficient setting latent lesion finite element unit in finite element model is optimized variable (its value is variable in simulation process), to damage two norms of the residual error of the strain statistical moment under the measured value of the strain statistical moment vector under state and emulation mode as objective function, Least-squares minimization algorithm is utilized to carry out Modifying model, make finite element model and truly damage error minimize between freely-supported part (i.e. two Norm minimums), when above-mentioned error reaches minimum, the numerical value of the stiffness coefficient of latent lesion finite element unit no longer changes, then can obtain a numerical value, the degree of injury of latent lesion finite element unit can be determined by this numerical value, this degree of injury is roughly the same with the degree of injury of the damage location of actual freely-supported part, therefore the degree of injury of the damage location on actual freely-supported part can be evaluated quantitatively by the degree of injury of latent lesion finite element unit.
Wherein, why strain statistical moment is chosen as damage criterion, and its theoretical foundation is as follows:
Under the effect that the freely-supported part of N number of degree of freedom encourages at white Gaussian noise, its equation of motion is:
Wherein A, C, K represent the mass matrix of freely-supported part, damping matrix and stiffness matrix respectively.The external load that f (t) is Gaussian distributed, concrete f (t)=[f
1(t), f
2(t) ..., f
n(t)], in this load vector, the power spectrum density of each element is constant S
0; X (t),
be respectively the displacement of freely-supported part, speed and vector acceleration.
The response of this freely-supported part is expressed as by mode superposition method,
Utilize the orthogonality of mode, the equation of motion of this freely-supported part can decoupling zero be one group of independently equation:
Wherein q
it () is canonical coordinates, be only the function of time; ω
ifor force transformation is to the frequency in frequency domain;
be the i-th rank generalized force,
it is the jth element in the i-th rank Mode Shape.
By using Fourier transform, can obtain the solution of equation (3) in frequency domain is:
Wherein
for generalized force p
ifourier transform, F (ω) is the Fourier transform of applied force on freely-supported part, k
i, m
iand c
ibe respectively the i-th rank modal stiffness, the i-th rank modal mass and the i-th rank modal damping.
The small deflection theory of and thin plate theoretical according to deflection of beam, there is following relation in the strain of its cross-sectional edge and amount of deflection:
Wherein x is the displacement (or claiming amount of deflection) of beam slab, and l is the coordinate along beam slab axis, h
0for the height of freely-supported part.
The solution of strain vector in frequency domain that equation (4) and equation (2) substitution equation (5) can be obtained each measuring point strain composition is:
Wherein,
for the frequency response function vector of each measuring point of freely-supported part, ψ
ifor strain mode.
For a kth measuring point, its power spectrum density is:
S
k(ω)＝ε(ω)ε
*(ω) (7)
The variance of the dynamic strain response of a kth measuring point is:
Show that the strain statistical moment of a kth measuring point is:
be the standard deviation of the strain time history of a kth measuring point, the strain time history of the measuring point that its value can be collected by dynamic date collecting device calculates.
Derive as can be seen from above, the quadravalence strain statistical moment of flexure type freely-supported part is the i-th rank modal stiffness k of freely-supported part
ifunction.When damage occurs freely-supported part, the change of freely-supported part modal stiffness can cause the change of strain statistical moment, can identify that freely-supported part damages by the change of this modal stiffness index, and thus straining statistical moment can as damage criterion.
Now there are some researches show, fourth central square obviously can reduce the impact of measurement noises for freely-supported part non-destructive tests effect, consider the susceptibility of strain data for local damage again, we finally choose the damage criterion of quadravalence strain statistical moment as freely-supported part of freely-supported part, below all referred to as strain statistical moment.Strain statistical moment under strain statistical moment under the nondestructive state mentioned in the present invention, the strain statistical moment under faulted condition and emulation mode can be calculated by formula (9).
The detailed process of described step (1) is as follows:
(1.1) on freely-supported part, get N number of uniform measuring point, stick foil gauge.
(1.2) utilize the excitational equipment that signal generator, power amplifier and vibrator form, apply the dynamic load of obeying white Gaussian noise distribution on freely-supported part top.
(1.3) utilize foil gauge, dynamic date collecting device gathers the dynamic strain response time-histories of freely-supported part.
The detailed process of described step (2) is as follows:
After there is damage in freely-supported part (freely-supported part is herein identical with the freely-supported part of step (1)), step (1.1) ~ (1.3) are repeated for damage freely-supported part, and notes for harmless freely-supported part and have the freely-supported part of damage to use identical white Gaussian noise sample.
The detailed process of described step (3) is as follows:
(3.1) formula (9) is utilized to calculate the strain statistical moment of harmless each measuring point of freely-supported part, composition nondestructive state strain statistical moment vector
(3.2) formula (9) is utilized to calculate the strain statistical moment of each measuring point of damage freely-supported part, composition faulted condition strain statistical moment vector
(3.3) formulae discovery is utilized to damage the change vector M of front and back freely-supported part strain statistical moment
c=M
c-M
u.
(3.4) for free beam, with the position of measuring point for X-axis coordinate, to strain statistical moment variable-quantity directional for Y-axis coordinate, curve plotting, potential latent lesion finite element unit is determined by the catastrophe point on curve; For simply supported slab, take point position as the coordinate in XY plane, to strain statistical moment variable quantity as Z coordinate, draw curved surface, determine latent lesion finite element unit by the Sudden change region on curved surface.
Described step should note following aspect in (4):
A () carries out dividing elements according to the position of measuring point uniform on freely-supported part, ensure that measuring point drops on cell node.
B (), for free beam, this method does not consider deep beam, i.e. the impact of detrusion can be ignored, so adopt Euler-Bernoulli beam element; For simply supported slab, adopt classical rectangular plate element.
C () Dynamic time history analysis adopts Newmark anomalous integral Ruili damping hypothesis, calculate the displacement of corresponding measuring point, and the strain of node needed for calculating according to equation (5) amount of deflection and the relation of strain.But notably in numerical evaluation, the second order of amount of deflection is reciprocal to be replaced with second order difference is approximate, that is:
The detailed process of described step (5) is as follows:
(5.1) according to the damage reason location result of (3) step, the stiffness coefficient of setting latent lesion finite element unit is optimized variable, and initial value is nondestructive state, is 1.Calculate the strain statistical moment of finite element model according to step (4), be called the assay value of strain statistical moment
(5.2) utilize least square method to carry out Modifying model, by adjusting the stiffness coefficient α of latent lesion finite element unit, (α is the identification stiffness matrix of latent lesion finite element unit
with harmless stiffness matrix k
eratio; When α is 1, illustrate that unit does not damage, as 0 < α < 1, the k that illustrates that unit there occurs (1-α)
edamage) make two Norm minimums that strain statistical moment measured value and analyze value difference, that is:
Min:||F||
2＝||Μ
a-M
m||
2
Note when freely-supported part unit is more, at Μ
aand M
min only get the strain statistical moment of Nodes on potential unit, to speed arithmetic speed, provide operational precision.
The computing formula of the i-th rank modal stiffness of freely-supported part is:
Wherein, k is the Bulk stiffness matrix of freely-supported part, by the element stiffness matrix k of each finite element unit
ecomposition; φ
ifor the i-th rank modal vector of freely-supported part,
for its transposition.
Stiffness coefficient α is the element stiffness matrix identified
with harmless element stiffness matrix k
eratio.Therefore, degree of injury can be evaluated by 1-α.
(5.3) the stiffness coefficient α of the potential unit identified is between 0-1, and 1-α is its degree of injury.
This method mainly gets uniform measuring point, the first step on overall freely-supported part, calculates the change of strain statistical moment before and after the damage of freely-supported part of these measuring points, carries out freely-supported part damage reason location; Second step, according to the freely-supported part damage reason location result of the first step, utilizes least-squares algorithm to carry out FEM updating, completes freely-supported part damage extent identification.
In sum, the non-destructive tests flow process that the present invention is based on the flexure type freely-supported part of freely-supported part strain statistical moment as shown in Figure 1, is specifically described below:
First on freely-supported part, uniform measuring point is got, white Gaussian noise excitation is applied to freely-supported part, obtain the dynamic strain time-histories of each measuring point, calculate the strain statistical moment of each measuring point before and after damage, be called the measured value of strain statistical moment, then according to the catastrophe point on change curve before and after its damage, on unit level, the damage position of freely-supported part is determined.
Then, according to the distribution of measuring point uniform on freely-supported part, set up the finite element model of freely-supported part, and simulate dynamic process, obtain corresponding measuring point strain statistical moment assay value, according to damage reason location result in the first step, the stiffness coefficient of setting latent lesion finite element unit is optimized variable, with two norms straining statistical moment measured value and assay value residual vector for objective function carries out Modifying model, the optimum results of the stiffness coefficient of latent lesion finite element unit is the recognition result of freely-supported part degree of injury.
Method provided by the invention for damage criterion is divided into two steps to carry out freely-supported part damage reason location and degree identification, obviously reduces the impact of measurement noises with the strain statistical moment of flexure type freely-supported part, improves the precision of damage reason location and degree identification, improves counting yield.
Below respectively using a free beam and unidirectional simply supported slab as the numerical example, the present invention is introduced, notices that the so-called numerical value in following example is software simulation gained.
1) free beam example
As shown in Figure 2, square 1 ~ 15 represents finite element unit for the size of free beam and white Gaussian noise incentive action position, and round dot 1 ~ 14 represents measuring point.Concrete, physical dimension is, span 3.0m, rectangular cross section height 0.2m, wide 0.3m.Its material behavior is, density 2500kg/m
3, elastic modulus 3 × 10
10pa, Poisson ratio 0.3.This free beam is divided into 15 isometric unit.Herein, the strain time history of measuring point 1-14 is only needed.The peak value of added white Gaussian noise is 200N, and frequency separation is 0-200Hz, and effect duration is 40s.
For checking the present invention, three kinds of operating condition of test are arranged to this free beam model.
The first operating mode, is designated as D0, and any damage does not occur freely-supported part;
The second operating mode, is designated as D1, and suppose that 10% damage occurs No. 6 unit, its element stiffness factor alpha is 0.9;
Under the third operating mode, be designated as D2, suppose that 30% damage all occurs No. 3, No. 6, No. 14 unit, its element stiffness factor alpha is 0.7.
When noting gathering dynamic strain time-histories three times, identical white Gaussian noise excitation is applied to freely-supported part.In order to verify the superiority of the present invention in antinoise, in the dynamic strain response time-histories under three kinds of operating modes, all with the addition of the measurement noises interference of 15%.
Step 1: under three kinds of operating condition of test, gathers the dynamic strain response time-histories of 14 measuring points respectively, forms three groups of vectors, is designated as respectively,
lower target numeral operating mode, upper target m is the abbreviation of measurement, represents the measured value of strain statistical moment.
Step 2: calculate each measuring point strain statistical moment changing value before and after damage respectively, composition of vector, is designated as respectively
subscript c is the abbreviation of change, represents the changing value of strain statistical moment.
Step 3: be numbered horizontal ordinate with measuring point,
with
for ordinate, draw the change curve of strain statistical moment, and according to the position of the catastrophe point determination latent lesion finite element unit on curve.As shown in Figure 3 a, 3 b.As can be seen from the figure, latent lesion finite element unit place, having there is obvious peak value in curve, can according to the position of this peak value determination latent lesion finite element unit.Measurement noises does not make curve occur ghost peak, tentatively describes the noise robustness of the method.
Step 4: set up its finite element model according to the position of measuring point on this free beam, and be divided into 15 isometric Euler-Bernoulli beam elements.The dynamic process of two damage regime in simulation steps 1, the strain statistical moment vector calculated under two kinds of damage regime is respectively
with
subscript a is the abbreviation of analysis, representative strain statistical moment assay value.According to the latent lesion finite element unit positioning scenarios in step 3, the stiffness coefficient of latent lesion finite element unit is set to optimized variable, to strain two norms of residual error between statistical moment assay value and measured value as objective function, utilize least-squares algorithm to carry out Modifying model, the degree of injury of latent lesion finite element unit can be judged according to the final optimization pass result of element stiffness coefficient.The identification situation of stiffness coefficient is as shown in Fig. 4 a, Fig. 4 b, and due to the impact of measurement noises, recognition result and the actual value of stiffness coefficient have certain error, concrete, in D1, the stiffness coefficient discre value of unit is 0.893, and degree of injury is 10.7%, and absolute error is 0.7%; In D2, the stiffness coefficient discre value of three latent lesion finite element unit is respectively 0.682,0.689,0.692, and degree of injury is respectively 31.8%, 31.1%, 30.8%, and absolute error is respectively 1.8%, 1.1%, 0.8%.Visible, owing to straining the good noise robustness of statistical moment, make free beam damage extent identification result have very little error.
2) simply supported slab example
As shown in Figure 5, each grid represents a finite element unit, and the intersection point between finite element is node for the physical dimension of simply supported slab and the position of latent lesion finite element unit, the position one_to_one corresponding of each measuring point on the position of each node and freely-supported part.Concrete, both direction span is 2.0m, and thickness of slab is 0.05m.Its material behavior is, density 7500kg/m
3, elastic modulus 2.1 × 10
11pa, Poisson ratio 0.3.This simply supported slab is divided into large unit such as 400 grades.If all 399 points of removing support place are strain measuring point.Note, because the flexibility of simply supported slab is comparatively large, the stress produced in order to avoid load is concentrated, and be employed herein uniform white Gaussian noise load, its peak value is 20Pa, and frequency separation is 0-200Hz, and effect duration is 40s.
For checking the present invention, three kinds of operating condition of test are arranged to this simply supported slab model.
The first operating mode, is designated as D0, and any damage does not occur freely-supported part;
The second operating mode, is designated as D1, and suppose that 10% damage occurs No. 3 unit, its element stiffness factor alpha is 0.9;
The third operating mode, is designated as D2, and suppose that the damage of 20%, 30%, 10% occurs No. 1, No. 2, No. 4 unit respectively, its element stiffness factor alpha is respectively 0.8,0.7,0.9.
When noting gathering dynamic strain time-histories three times, identical white Gaussian noise excitation is applied to freely-supported part.In order to verify the superiority of the present invention in antinoise, in the dynamic strain response time-histories under three kinds of operating modes, all with the addition of the measurement noises interference of 15%.
Repeat the step 1 ~ step 4 in free beam example.But there is any should be noted that, due to the node on this simply supported slab finite element model comparatively free beam measuring point number greatly increase, perform step 4 time, only get the strain statistical moment of latent lesion finite element unit four angle points, reduce the impact of extraneous data, improve computational accuracy and efficiency.
Latent lesion finite element unit positioning result is shown in Fig. 6 a, Fig. 6 b, even if visible noise still show clearly the position of latent lesion finite element unit up to the catastrophe point of 15%, figure mean camber.
The result of damage extent identification is shown in Fig. 7 a, Fig. 7 b, and in D1, latent lesion finite element unit stiffness coefficient recognition result is 0.806, and identification of damage degree is 19.4%, and absolute error is 9.4%; In D2, latent lesion finite element unit stiffness coefficient discre value is respectively 0.713,0.620,0.803, identification of damage degree is respectively 28.7%, 38.0%, 19.7%, absolute error is respectively 8.7%, 8.0%, 9.7%, because this freely-supported part degree of freedom increases greatly compared to free beam, error is corresponding increasing also.Even if but measurement noises impact up to 15% time, the maximum error of damage extent identification is not also more than 10%, and this is acceptable result at engineering field.
Above two kinds of freely-supported parts, in four kinds of damage regime, the freely-supported part damnification recognition method based on strain statistical moment that the present invention proposes correctly have identified latent lesion finite element unit position and degree of injury effectively.
To when having the tested freely-supported part of damage to detect in practical operation, can according to five above-mentioned steps, the first step first encourages a harmless freely-supported part exemplar and measures in advance, second step is again to there being the tested freely-supported part of damage encourage and measure, the follow-up measurement that can be completed degree of injury again by finite element analysis, the degree of injury of the latent lesion finite element unit that finite element analysis obtains is the operational degree of the defective component of tested freely-supported part.
Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.
Claims (6)
1., based on a freely-supported part damnification recognition method for strain statistical moment, it is characterized in that comprising the following steps:
1) on freely-supported part uniform multiple foil gauge as measuring point, applying white Gaussian noise encourages, what under the harmless vector sum faulted condition that the strain statistical moment obtaining freely-supported part each measuring point under nondestructive state respectively forms, the strain statistical moment of each measuring point was formed damages vector, calculate the change vector of strain statistical moment of each measuring point before and after damage and curve plotting, according to the damage location on the mutated site determination freely-supported part of curve;
2) set up the finite element model of freely-supported part and divide finite element unit, each node of finite element unit is corresponding with the position of each measuring point on freely-supported part, simulation and step 1) identical dynamic process, obtain the analysis that the strain statistical moment of each node is formed under emulation mode vectorial;
3) according to step 1) damage location of locating, the stiffness coefficient arranging latent lesion finite element unit finite element model corresponding to damage location position is optimized variable, analyzing vector with two norms of the residual error damaging vector is objective function, least square method is utilized to carry out Modifying model, make two Norm minimums, obtain the degree of injury of latent lesion finite element unit, this extent of damage is the degree of injury of damage location on freely-supported part.
2. a kind of freely-supported part damnification recognition method based on strain statistical moment according to claim 1, is characterized in that step 1) in the number of measuring point of arranging be N number of, then the strain statistical moment of a kth measuring point is
Wherein
the standard deviation of the strain time history of a kth measuring point, k≤N and
Wherein S
k(ω) be the power spectrum density of a kth measuring point, and
S
k(ω)＝ε(ω)ε
*(ω)
Wherein ε (ω) is the solution of strain vector in frequency domain of each measuring point strain composition, and
Wherein, q
ifor canonical coordinates and
for the i-th rank displacement modes of freely-supported part, F (ω) is the Fourier transform of applied force on freely-supported part, ω be force transformation to the frequency in frequency domain, k
i, m
iand c
ibe respectively the i-th rank modal stiffness, the i-th rank modal mass and the i-th rank modal damping; ψ
ifor strain mode and
wherein
for the i-th rank displacement modes of freely-supported part, l is along answering nyctitropic length variable, h
0for the thickness of freely-supported part.
3. a kind of freely-supported part damnification recognition method based on strain statistical moment according to claim 1, it is characterized in that described step 1) in utilize excitational equipment to encourage, described excitational equipment comprises signal generator, power amplifier and vibrator, and described excitational equipment applies the dynamic load of obeying white Gaussian noise distribution on the top of freely-supported part; Foil gauge gathers its dynamic strain response time-histories by dynamic date collecting device.
4. a kind of freely-supported part damnification recognition method based on strain statistical moment according to claim 1, is characterized in that step 3) comprise the following steps:
3.1) according to the positioning result of damage location on freely-supported part, setting is optimized variable with the stiffness coefficient of the latent lesion finite element unit of the damage location corresponding position on freely-supported part, and this optimized variable initial value is nondestructive state, and value is 1; Calculate the strain statistical moment of finite element model;
3.2) least square method is utilized to carry out Modifying model, by adjusting the stiffness coefficient α of latent lesion finite element unit on finite element model, make two Norm minimums of the residual error of the strain statistical moment of each measuring point under the strain statistical moment of each node and faulted condition;
3.3) the stiffness coefficient α of the latent lesion finite element unit identified is between 0 ~ 1, and then the degree of injury obtaining damage location on latent lesion finite element unit and freely-supported part is 1-α.
5. a kind of freely-supported part damnification recognition method based on strain statistical moment according to claim 1, is characterized in that step 3) in the finite element model of freely-supported part adopt Euler-Bernoulli beam element or rectangular plate element.
6. a kind of freely-supported part damnification recognition method based on strain statistical moment according to claim 1, it is characterized in that step 3) medium power time-history analysis employing Newmark anomalous integral Ruili damping hypothesis, calculate the displacement of measuring point, and the strain of relation computing node according to amount of deflection and strain.
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