CN103971018A - Method for node rigidity prediction based on vibration measurement - Google Patents
Method for node rigidity prediction based on vibration measurement Download PDFInfo
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- CN103971018A CN103971018A CN201410220566.5A CN201410220566A CN103971018A CN 103971018 A CN103971018 A CN 103971018A CN 201410220566 A CN201410220566 A CN 201410220566A CN 103971018 A CN103971018 A CN 103971018A
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Abstract
The invention relates to a method for node rigidity prediction based on vibration measurement. The method is characterized by comprising the steps of first establishing a node model (a finite element model or a test model), utilizing the model to enable a first principal component score extreme value obtained through generalized likelihood ratio principal component analysis to serve as a control index, and establishing a relation curve of the proportion of the control index exceeding the upper limit and the lower limit and node rigidity under different damage working conditions in a statistical quality control chart; in actual engineering, measuring vibration response of a node, and calculating the proportion of the control index exceeding the upper limit and the lower limit in the statistical quality control chart according to the response; and finally substituting the proportion of the control index exceeding the upper limit and the lower limit into the relation curve to predict the node rigidity. According to the method, the node rigidity can be rapidly and effectively predicted without needing other data, only acceleration response of a structure needs collecting, and the method can be used for structural ageing and after-calamity rapid prediction.
Description
Technical field
The present invention relates to a kind of technology to the prediction of node rigidity, particularly the technology to the prediction of node rigidity in a kind of structure use procedure, i.e. a kind of node Stiffness Prediction method based on vibration-testing.
Background technology
For avoiding the pernicious of bridge pier to collapse, improve its kinematic behavior, reduce long-term integrated maintenance expense, bridge structural damage identification and evaluation based on dynamic test become study hotspot.But all there is limitation separately in the various diagnosing structural damage methods based on vibration-testing at present, owing to can only obtain the former order frequencies of structure minority and the vibration shape in actual test condition, it is more coarse therefore directly utilizing frequency or the vibration shape to damage identification.Many scholars seek a kind ofly to damaging the variation of responsive index, to diagnose damage for this reason.Thereby mainly current state and health status are made comparisons to judgement current state.
In the last few years, considered that the damage recognition technology of uncertain factor obtained certain applications in vibration-testing, particularly in and large-span structure large-scale at some.But current research mainly concentrates on and utilizes corresponding sensitive indicator to judge whether structure has damage from structural vibration information, and training sample wherein is mainly confined to finite element model.But in practical application there is the defect of himself in finite element model.And relate to less for the information such as stiffness variation of directly utilizing vibration information to extract structure.There is the beginning of this century scholar to propose to utilize the Damage Assessment Method technology of statistical knowledge to be developed, but still there is following problem in it: (1) current, and to utilize the index that statistical knowledge is mainly considered be acceleration itself, but index while there is the large problem of interference affected by environment due to acceleration self is unreliable; (2) utilize the structural damage technology of statistical knowledge not combine with the rigidity of structure.
Based on above situation, the present invention proposes that a kind of to take CENERALIZED POLAR likelihood ratio principal component scores maximal value and minimum value be to control the technology of index, thereby and it is applied to the ratio that statistical process control proposes to exceed with statistical process control index upper and lower boundary in conjunction with the relation curve of expection, carry out the method for predict later stage rigidity.
Summary of the invention
The object of the present invention is to provide a kind of node Stiffness Prediction method based on vibration-testing that can fast and effeciently predict the rigidity of node.
For achieving the above object, technical scheme of the present invention is: a kind of node Stiffness Prediction method based on vibration-testing, the finite element model of model node or test model, utilize subsequently this model to using the first principal component score extreme value of CENERALIZED POLAR likelihood ratio principal component analysis (PCA) as controlling index, and in Statistical quality control chart, set up the relation curve that described control index under different damage operating modes exceeds ratio and the node rigidity of upper and lower boundary; Secondly, in Practical Project, the vibratory response of measured node, controls the ratio that index exceeds upper and lower boundary in RESPONSE CALCULATION Statistical quality control chart according to this; Thereby the ratio substitution relation curve prediction node rigidity that finally this control index is exceeded to upper and lower boundary;
The described detailed process that goes out first principal component score extreme value with the principal component analysis (PCA) of CENERALIZED POLAR likelihood ratio, comprises the following steps,
S1: gather the instantaneous acceleration response of structure under the node health status of described model
mgroup;
S2: by before the acceleration responsive of structure under health status
mgroup, as with reference to sample H
0, wherein,
m<
m, Mwith
mfor natural number;
S3: at hypothesis H
0in situation, calculate H
0covariance matrix Σ and inverse matrix Γ and error covariance matrix Ф, that is:
Suppose that successively each sensor is estimated signal, based on least mean-square error, estimate that MMSE utilizes remaining sensor to estimate it, meanwhile, sensor signal
xbe divided into normal signal
vestimated signal with hypothesis
u, that is:
Calculate thus separated covariance matrix Σ
For saving computing time and simplifying computation process, ask the inverse matrix Γ of Σ:
Error covariance matrix is:
S4: will remove H under nondestructive state
0outer acceleration responsive
m-Mgroup is as measuring sample H
1;
S5: at hypothesis H
1in situation, calculate H
1covariance matrix Σ and inverse matrix Γ and the error covariance matrix Ф of covariance matrix;
S6: calculate each sample according to following formula
p(
u/
v; H
0) and
p(
u/
v; H
1), wherein,
p(
u/
v; H
i ) be
h i (
i=0,1) probability density of supposing,
Wherein:
μ u for the sample average of hypothesis estimation,
μ v refer to the intact sample average of residue,
e(
μ/
v) refer to expectation value;
S7: calculate CENERALIZED POLAR likelihood ratio S according to following formula;
S8: adopt principal component analysis (PCA) to carry out dimensionality reduction to the CENERALIZED POLAR likelihood ratio S of all measurement samples, this CENERALIZED POLAR likelihood ratio S contains
noK,
rrow; Wherein,
nfor number of sensors,
rfor sampling number, and extract first principal component score and first suppose that every group of sample number of principal component analysis (PCA) is
p, be divided into
l=
r/pgroup, to each grouping matrix S
g(
g=1,2 ...,
l) carry out respectively standardization, establish S
gfor
Wherein, S
ncorresponding the
nindividual sensor performance degeneration CENERALIZED POLAR likelihood ratio, S
gmatrix X after standardization
gfor
s ij for CENERALIZED POLAR likelihood ratio sub matrix S
gin
irow
jrow;
s ik for CENERALIZED POLAR likelihood ratio sub matrix S
gin
irow
krow;
Wherein:
l,
r,
n,
pbe natural number;
For simplifying computation process, to get first principal component each variable of raw sample data is evaluated, first principal component is F
1
Wherein: (
u 11,
u 12...,
u 1n) be first eigenvector;
Because each element score of first principal component and first principal component score corresponding element differ a constant, so use first principal component score at this
score gvariable is evaluated;
?
score gcan change to:
Wherein,
be
nthe corresponding first principal component score of individual sensor, wherein,
nfor natural number, with first principal component score maximal value
and minimum value
as the control index of drawing sensor performance degeneration detection control chart
iNDEX; S
gfirst principal component score extreme value be
index gmaxwith
index gmin:
As all subgroup S
g(
g=1,2 ...,
l) all complete principal component analysis (PCA), the control index of S
iNDEXfor
。
In embodiments of the present invention, thereby the described detailed process that exceeds the ratio substitution relation curve prediction node rigidity of upper and lower boundary according to control index comprises the following steps,
S21: the boundary line up and down of drawing Statistical quality control chart according to following formula: in this setup control index
iNDEXsubgroup sample
indexnumber is
k, subgroup number
n=
l/
k; Therefore,
iNDEXaverage sampling sample
x 1,
x 2,
x nbasic obedience
z~ N (
μ,
σ 2 / k) normal distribution, wherein,
k, N, lbe natural number;
x jcomprise
x jmaxand
x jmin;
According to Gaussian distribution, the fiducial interval of the upper and lower boundary of as if statistics quality control chart is 1-
,
for level of significance, the upper boundary of Statistical quality control chart
uCLand Lower Limits
lCLbe respectively:
Wherein,
zrepresent boundary in Gaussian distribution
uCLcontain
uCL maxand
uCL min, Lower Limits
lCLcontain
lCL maxand
lCL min;
It is Gaussian distributed
zthe value probability that drops on fiducial interval be 1-
;
But,
μwith
σoccurrence unknown, can only estimate it, try to achieve upper and lower boundary
uCLwith
lCL:
Wherein,
comprise
with
,
a 2value is relevant with sample size,
comprise
with
, specific as follows:
Wherein,
r jcontain
r j, maxwith
r j, min,
r j, maxcomputing formula is as follows, in like manner, can calculate
r j, min:
S22: gather the
iplant the acceleration responsive of structure under damage operating mode as measuring sample H
i ;
S23: repeating said steps S1 to S8, wherein, H
1by H
i replace, and in Statistical quality control chart, add the boundary line up and down in described step S21;
S24: calculate the according to Statistical quality control chart
iplant under operating mode and control the ratio that index exceeds upper and lower boundary line;
S25: calculate the
iplant secant rigidity under operating mode,
In formula:
be
iinferior circulation is forward and reverse while loading corresponding peak point load;
be
icorresponding peak point displacement that inferior circulation is forward and reverse while loading;
S26: exceed the ratio in upper and lower boundary line and the secant rigidity opening relationships curve of step S25 according to the control index under the different operating modes of step S24;
S27: gather the acceleration responsive of member to be measured, suppose that sample is H
i ;
S28: repeating step S4 is to step S8, wherein, H
1by H
i replace, and in Statistical quality control chart, add the boundary line up and down in described step S21; According to Statistical quality control chart, calculate it simultaneously and control the ratio that index exceeds upper and lower boundary line;
S29: thereby by ratio substitution relation curve prediction rigidity.
Compared to prior art, the present invention has following beneficial effect:
1, the technology of the present invention is directly utilized acceleration signal, succinctly convenient;
2, the technology of the present invention has proposed a kind of broad sense and likelihood ratio principal component scores maximal value and minimum value statistical process control as control index of take;
3, the rigidity of the technology of the present invention energy fast prediction node.
Accompanying drawing explanation
Fig. 1 is the hysteresis loop of embodiment of the present invention CFFT post power-displacement.
Fig. 2 is the embodiment of the present invention (healthy operating mode) Statistical quality control chart.
Fig. 3 is the embodiment of the present invention (damage operating mode one) Statistical quality control chart.
Fig. 4 is the embodiment of the present invention (damage operating mode two) Statistical quality control chart.
Fig. 5 is the embodiment of the present invention (damage operating mode three) Statistical quality control chart.
Fig. 6 is the embodiment of the present invention (damage operating mode four) Statistical quality control chart.
Embodiment
Below in conjunction with accompanying drawing, technical scheme of the present invention is specifically described.
The present invention is a kind of node Stiffness Prediction method based on vibration-testing, the model (finite element model or test model) of model node (bean column node, pier stud plastic hinge etc.), utilize subsequently this model to using the first principal component score extreme value of CENERALIZED POLAR likelihood ratio principal component analysis (PCA) as controlling index, and in Statistical quality control chart, set up the relation curves that the lower described control index of different damage operating modes (different node rigidity) exceeds ratio and the node rigidity of upper and lower boundary; Secondly, in Practical Project, the vibratory response of measured node, controls the ratio that index exceeds upper and lower boundary in RESPONSE CALCULATION Statistical quality control chart according to this; Thereby the ratio substitution relation curve prediction node rigidity that finally this control index is exceeded to upper and lower boundary;
The described detailed process that goes out first principal component score extreme value with the principal component analysis (PCA) of CENERALIZED POLAR likelihood ratio, comprises the following steps,
S1: gather the instantaneous acceleration response of structure under the node health status of described model
mgroup;
S2: by before the acceleration responsive of structure under health status
mgroup, as with reference to sample H
0, wherein,
m<
m, Mwith
mfor natural number;
S3: at hypothesis H
0in situation, calculate H
0covariance matrix Σ and inverse matrix Γ and error covariance matrix Ф, that is:
Suppose that successively each sensor is estimated signal, based on least mean-square error, estimate that MMSE utilizes remaining sensor to estimate it, meanwhile, sensor signal
xbe divided into normal signal
vestimated signal with hypothesis
u, that is:
Calculate thus separated covariance matrix Σ
For saving computing time and simplifying computation process, ask the inverse matrix Γ of Σ:
Error covariance matrix is:
S4: will remove H under nondestructive state
0outer acceleration responsive
m-Mgroup is as measuring sample H
1;
S5: at hypothesis H
1in situation, calculate H
1covariance matrix Σ and inverse matrix Γ and the error covariance matrix Ф of covariance matrix;
S6: calculate each sample according to following formula
p(
u/
v; H
0) and
p(
u/
v; H
1), wherein,
p(
u/
v; H
i ) be
h i (
i=0,1) probability density of supposing, (wherein, H
1: suppose H
1in situation, H
0: suppose H
0in situation)
Wherein:
μ u for the sample average of hypothesis estimation,
μ v refer to the intact sample average of residue,
e(
μ/
v) refer to expectation value;
S7: calculate CENERALIZED POLAR likelihood ratio S according to following formula;
S8: adopt principal component analysis (PCA) to carry out dimensionality reduction to the CENERALIZED POLAR likelihood ratio S of all measurement samples, this CENERALIZED POLAR likelihood ratio S contains
noK,
rrow; Wherein,
nfor number of sensors,
rfor sampling number, and extract first principal component score and first suppose that every group of sample number of principal component analysis (PCA) is
p, be divided into
l=
r/pgroup, to each grouping matrix S
g(
g=1,2 ...,
l) carry out respectively standardization, establish S
gfor
Wherein, S
ncorresponding the
nindividual sensor performance degeneration CENERALIZED POLAR likelihood ratio, S
gmatrix X after standardization
gfor
s ij for CENERALIZED POLAR likelihood ratio sub matrix S
gin
irow
jrow;
s ik for CENERALIZED POLAR likelihood ratio sub matrix S
gin
irow
krow;
Wherein:
l,
r,
n,
pbe natural number;
For simplifying computation process, to get first principal component each variable of raw sample data is evaluated, first principal component is F
1
Wherein: (
u 11,
u 12...,
u 1n) be first eigenvector;
Because each element score of first principal component and first principal component score corresponding element differ a constant, so use first principal component score at this
score gvariable is evaluated;
?
score gcan change to:
Wherein,
be
nthe corresponding first principal component score of individual sensor, wherein,
nfor natural number, with first principal component score maximal value
and minimum value
as the control index of drawing sensor performance degeneration detection control chart
iNDEX; S
gfirst principal component score extreme value be
index gmaxwith
index gmin:
As all subgroup S
g(
g=1,2 ...,
l) all complete principal component analysis (PCA), the control index of S
iNDEXfor
。
Thereby the described detailed process that exceeds the ratio substitution relation curve prediction node rigidity of upper and lower boundary according to control index, comprises the following steps,
S21: the boundary line up and down of drawing Statistical quality control chart according to following formula: in this setup control index
iNDEXsubgroup sample
indexnumber is
k, subgroup number
n=
l/
k; Therefore,
iNDEXaverage sampling sample
x 1,
x 2,
x nbasic obedience
z~ N (
μ,
σ 2 / k) normal distribution, wherein,
k, N, lbe natural number;
x jcomprise
x jmaxand
x jmin;
According to Gaussian distribution, the fiducial interval of the upper and lower boundary of as if statistics quality control chart is 1-
,
for level of significance, the upper boundary of Statistical quality control chart
uCLand Lower Limits
lCLbe respectively:
Wherein,
zrepresent boundary in Gaussian distribution
uCLcontain
uCL maxand
uCL min, Lower Limits
lCLcontain
lCL maxand
lCL min;
Be Gaussian distributed (
z) the value probability that drops on fiducial interval be 1-
;
But,
μwith
σoccurrence unknown, can only estimate it, try to achieve upper and lower boundary
uCLwith
lCL:
Wherein,
comprise
with
,
a 2value is relevant with sample size,
comprise
with
, specific as follows:
Wherein,
r jcontain
r j, maxwith
r j, min,
r j, maxcomputing formula is as follows, in like manner, can calculate
r j, min:
S22: gather the
iplant the acceleration responsive of structure under damage operating mode as measuring sample H
i ;
S23: repeating said steps S1 to S8, wherein, H
1by H
i replace, and in Statistical quality control chart, add the boundary line up and down in described step S21;
S24: calculate the according to Statistical quality control chart
iplant under operating mode and control the ratio that index exceeds upper and lower boundary line;
S25: calculate the
iplant secant rigidity under operating mode,
In formula:
be
iinferior circulation is forward and reverse while loading corresponding peak point load;
be
icorresponding peak point displacement that inferior circulation is forward and reverse while loading;
S26: exceed the ratio in upper and lower boundary line and the secant rigidity opening relationships curve of step S25 according to the control index under the different operating modes of step S24;
S27: gather the acceleration responsive of member to be measured, suppose that sample is H
i ;
S28: repeating step S4 is to step S8, wherein, H
1by H
i replace, and in Statistical quality control chart, add the boundary line up and down in described step S21; According to Statistical quality control chart, calculate it simultaneously and control the ratio that index exceeds upper and lower boundary line;
S29: thereby by ratio substitution relation curve prediction rigidity.
So far, according to above step, can realize and utilize acceleration to predict fast its rigidity to node.
Below tell about specific embodiments of the invention.
Concrete, with the pseudo-static experimental model of a FRP pipe constraint RC post, the present invention is described.The pier stud size diameter of test is 320mm, and pier shaft clear height is 1300mm.Test adopts transient state hammer stimulating, after excitation input each time, treats that acceleration responsive substantially steadily approaches null value and just starts to encourage next time.Fig. 1 manages load-displacement lagging curve of reinforced column for FRP.
(1) first to structure, in starting stage, surrender stage 1D, 4D, 6D, 8D collection power acceleration at different levels, respond respectively;
(2) consider the impact of environment, therefore front 200 collection points, place are respectively knocked in intercepting;
(3) consider that in hammering method, percussion power is not quite similar, therefore the acceleration collecting is carried out to standardization by following formula;
Wherein,
xfor the acceleration responsive after processing,
x 0for the acceleration responsive gathering,
for acceleration responsive average;
(4) utilize the control index calculation procedure that the present invention proposes to calculate the control desired value under different operating modes;
(5) that utilizes that the present invention proposes draws Statistical quality control chart step and draws the quality control chart under different operating modes to control index, the results are shown in Figure 2 ~ Fig. 6 and table 1.Consider that the sample gathering in test is less, every 20 groups of this example carries out dimensionality reduction, and establishing each subgroup sample number is 5, known
a 2=0.577.Last group of number of Statistical quality control chart is shown in following formula so:
Sampling number ÷ dimensionality reduction number (20) ÷ subgroup sample number (5);
(6) set up FRP pipe constraint RC post related function, thereby can utilize the dynamic test in early stage of this class A of geometric unitA to predict the later stage rigidity of this class A of geometric unitA.
Fig. 2 ~ Fig. 6 is the Statistical quality control chart under each stage, displacement along with CYCLIC LOADING increases as seen from the figure, in control chart, control index and exceed counting also along with increasing of upper and lower boundary, again verified and take CENERALIZED POLAR likelihood ratio root mean square principal component analysis (PCA) first principal component score max min as controlling the feasibility of index.Its statistics count, break bounds ratio, rigidity etc. the results are shown in Table 1.
As shown in Table 1, along with the increase of the ratio of breaking bounds, stiffness of structural member is index decreased.Therefore, the rigidity drawing according to the ratio that breaks bounds calculating in different operating mode quality control charts and pseudo-static experimental, by least-square fitting approach, obtains rigidity of structure expression formula and sees following formula:
Can find out that the rigidity and the practical stiffness that calculate are more identical.
Be more than preferred embodiment of the present invention, all changes of doing according to technical solution of the present invention, when the function producing does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.
Claims (2)
1. the node Stiffness Prediction method based on vibration-testing, it is characterized in that: the finite element model of model node or test model, utilize subsequently this model to using the first principal component score extreme value of CENERALIZED POLAR likelihood ratio principal component analysis (PCA) as controlling index, and in Statistical quality control chart, set up the relation curve that described control index under different damage operating modes exceeds ratio and the node rigidity of upper and lower boundary; Secondly, in Practical Project, the vibratory response of measured node, controls the ratio that index exceeds upper and lower boundary in RESPONSE CALCULATION Statistical quality control chart according to this; Thereby the ratio substitution relation curve prediction node rigidity that finally this control index is exceeded to upper and lower boundary;
The detailed process of the described first principal component score extreme value with the principal component analysis (PCA) of CENERALIZED POLAR likelihood ratio, comprises the following steps,
S1: gather the instantaneous acceleration response of structure under the node health status of described model
mgroup;
S2: by before the acceleration responsive of structure under health status
mgroup, as with reference to sample H
0, wherein,
m<
m, Mwith
mfor natural number;
S3: at hypothesis H
0in situation, calculate H
0covariance matrix Σ and inverse matrix Γ and error covariance matrix Ф, that is:
Suppose that successively each sensor is estimated signal, based on least mean-square error, estimate that MMSE utilizes remaining sensor to estimate it, meanwhile, sensor signal
xbe divided into normal signal
vestimated signal with hypothesis
u, that is:
Calculate thus separated covariance matrix Σ:
For saving computing time and simplifying computation process, ask the inverse matrix Γ of Σ:
Error covariance matrix is:
S4: will remove H under nondestructive state
0outer acceleration responsive
m-Mgroup is as measuring sample H
1;
S5: at hypothesis H
1in situation, calculate H
1covariance matrix Σ and inverse matrix Γ and the error covariance matrix Ф of covariance matrix;
S6: calculate each sample according to following formula
p(
u/
v; H
0) and
p(
u/
v; H
1), wherein,
p(
u/
v; H
i ) be
h i (
i=0,1) probability density of supposing,
Wherein:
μ u for the sample average of hypothesis estimation,
μ v refer to the intact sample average of residue,
e(
μ/
v) refer to expectation value;
S7: calculate CENERALIZED POLAR likelihood ratio S according to following formula;
S8: adopt principal component analysis (PCA) to carry out dimensionality reduction to the CENERALIZED POLAR likelihood ratio S of all measurement samples, this CENERALIZED POLAR likelihood ratio S contains
noK,
rrow; Wherein,
nfor number of sensors,
rfor sampling number, and extract first principal component score and first suppose that every group of sample number of principal component analysis (PCA) is
p, be divided into
l=
r/pgroup, to each grouping matrix S
g(
g=1,2 ...,
l) carry out respectively standardization, establish S
gfor
Wherein, S
ncorresponding the
nindividual sensor performance degeneration CENERALIZED POLAR likelihood ratio, S
gmatrix X after standardization
gfor
s ij for CENERALIZED POLAR likelihood ratio sub matrix S
gin
irow
jrow;
s ik for CENERALIZED POLAR likelihood ratio sub matrix S
gin
irow
krow;
Wherein:
l,
r,
n,
pbe natural number;
For simplifying computation process, to get first principal component each variable of raw sample data is evaluated, first principal component is F
1
Wherein: (
u 11,
u 12...,
u 1n) be first eigenvector;
Because each element score of first principal component and first principal component score corresponding element differ a constant, so use first principal component score at this
score gvariable is evaluated;
?
score gcan change to:
Wherein,
be
nthe corresponding first principal component score of individual sensor, wherein,
nfor natural number;
With first principal component score maximal value
and minimum value
as the control index of drawing sensor performance degeneration detection control chart
iNDEX; S
gfirst principal component score extreme value be
index gmaxwith
index gmin:
As all subgroup S
g(
g=1,2 ...,
l) all complete principal component analysis (PCA), the control index of S
iNDEXfor
。
2. the node Stiffness Prediction method based on vibration-testing according to claim 1, is characterized in that: thus describedly according to the detailed process of controlling index and exceed the ratio substitution relation curve prediction node rigidity of upper and lower boundary, comprise the following steps,
S21: the boundary line up and down of drawing Statistical quality control chart according to following formula: in this setup control index
iNDEXsubgroup sample
indexnumber is
k, subgroup number
n=
l/
k; Therefore,
iNDEXaverage sampling sample
x 1,
x 2,
x nbasic obedience
z~ N (
μ,
σ 2 / k) normal distribution, wherein,
k, N, lbe natural number;
x jcomprise
x jmaxand
x jmin;
According to Gaussian distribution, the fiducial interval of the upper and lower boundary of as if statistics quality control chart is 1-
,
for level of significance, the upper boundary of Statistical quality control chart
uCLand Lower Limits
lCLbe respectively:
Wherein,
zrepresent boundary in Gaussian distribution
uCLcontain
uCL maxand
uCL min, Lower Limits
lCLcontain
lCL maxand
lCL min;
It is Gaussian distributed
zthe value probability that drops on fiducial interval be 1-
;
But,
μwith
σoccurrence unknown, can only estimate it, try to achieve upper and lower boundary
uCLwith
lCL:
Wherein,
comprise
with
,
a 2value is relevant with sample size,
comprise
with
, specific as follows:
Wherein,
r jcontain
r j, maxwith
r j, min,
r j, maxcomputing formula is as follows, in like manner, can calculate
r j, min:
S22: gather the
iplant the acceleration responsive of structure under damage operating mode as measuring sample H
i ;
S23: repeating said steps S1 to S8, wherein, H
1by H
i replace, and in Statistical quality control chart, add the boundary line up and down in described step S21;
S24: calculate the according to Statistical quality control chart
iplant under operating mode and control the ratio that index exceeds upper and lower boundary line;
S25: calculate the
iplant secant rigidity under operating mode,
In formula:
be
iinferior circulation is forward and reverse while loading corresponding peak point load;
be
icorresponding peak point displacement that inferior circulation is forward and reverse while loading;
S26: exceed the ratio in upper and lower boundary line and the secant rigidity opening relationships curve of step S25 according to the control index under the different operating modes of step S24;
S27: gather the acceleration responsive of member to be measured, suppose that sample is H
i ;
S28: repeating step S4 is to step S8, wherein, H
1by H
i replace, and in Statistical quality control chart, add the boundary line up and down in described step S21; According to Statistical quality control chart, calculate it simultaneously and control the ratio that index exceeds upper and lower boundary line;
S29: thereby by ratio substitution relation curve prediction rigidity.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN108573224B (en) * | 2018-04-04 | 2021-07-23 | 暨南大学 | Bridge structure damage positioning method for mobile reconstruction of principal components by using single sensor information |
| CN114252107A (en) * | 2021-12-22 | 2022-03-29 | 河南省国安建筑工程质量检测有限公司 | Beam type structure quality monitoring system using optical fiber sensing |
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