CN111125824A - Structural damage identification method based on deletion model - Google Patents

Structural damage identification method based on deletion model Download PDF

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CN111125824A
CN111125824A CN201911373177.5A CN201911373177A CN111125824A CN 111125824 A CN111125824 A CN 111125824A CN 201911373177 A CN201911373177 A CN 201911373177A CN 111125824 A CN111125824 A CN 111125824A
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朱瑞虎
王启明
郑金海
王宁
罗孟岩
车宇飞
王军磊
曾海坤
郭健
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Hohai University HHU
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Abstract

The invention discloses a structural damage identification method based on a deletion model, which comprises the following steps: obtaining the curvature modal difference between the current state and the intact state of the structure; establishing a curvature modal difference regression model, and matrixing the regression model; performing parameter estimation on the matrixed regression model; deleting the curvature modal difference of an observation point, reestablishing a regression model, matrixing and carrying out parameter estimation; analyzing the difference of regression coefficients before and after the observation point is deleted by using WK statistic, and judging whether the point of the structure is damaged; and deleting the observation points in sequence, and judging whether all the observation points of the structure are damaged. The invention can solve the technical problem that the judgment of the damage position is not clear due to noise and measurement error in the conventional dynamic damage identification.

Description

Structural damage identification method based on deletion model
Technical Field
The invention relates to the technical field of engineering detection, in particular to a structural damage identification method based on a deletion model.
Background art:
the damage research method based on the dynamic fingerprint comprehensively utilizes interdisciplinary technologies such as a structure vibration theory, a vibration testing technology, a data processing technology and the like, and is considered to be the most promising structure nondestructive testing method at present. In the dynamic fingerprint damage diagnosis method, the curvature mode shows high sensitivity of local damage, and the method becomes a hotspot of research in the structural engineering field. But the curvature mode sensitivity is high, and the index is easily influenced by random errors and measurement errors, so that the robustness of the index is poor.
Disclosure of Invention
The invention aims to provide a structural damage identification method based on a deletion model, which aims to solve the defect that damage position judgment is not clear due to noise and measurement error in the prior art.
A structural damage identification method based on a deletion model comprises the following steps:
obtaining the curvature modal difference between the current state and the intact state of the structure;
constructing a regression model according to the curvature modal difference, and performing parameter estimation after matrixing the regression model;
deleting curvature modal differences of a plurality of observation points, rebuilding a regression model, matrixing the regression model and then performing parameter estimation;
and calculating the WK value before and after the observation point is deleted according to the parameter estimation result, and judging whether the point is the damage in the structure or not according to the WK value.
Further, the method for acquiring the curvature modal difference comprises the following steps:
obtaining an initial curvature mode of the structure through a vibration test;
regularly observing the curvature mode of the current state;
and comparing the current curvature mode with the curvature mode in the intact state to obtain the curvature mode difference.
Further, the method for constructing the regression model according to the curvature modal difference and matrixing the regression model comprises the following steps:
let observation data be { xi，yi}，i＝1，2，…，n；
Wherein xiNumbering the measuring points, yiIs the curvature mode difference of the corresponding unit;
establishing a regression model:
Figure BDA0002340228580000021
vector of independent variables
Figure BDA0002340228580000022
Coefficient vector β ═ (β)0，β1，β2，β3)T；
The model can be written in matrix form:
Y＝Xβ+ε；
wherein Y is (Y)1，y2，…，yn)T；ε＝(ε1，ε2，…εn)TThe random error vector satisfies the white noise condition; x is an n X4 order matrix with the ith action
Figure BDA0002340228580000023
Further, the method for performing parameter estimation on the matrixed regression model comprises the following steps:
finding an estimate of the parameter β using a least squares estimation method
Figure BDA0002340228580000024
The sum of the squares of the errors of the following equations:
Figure BDA0002340228580000025
the minimum is reached;
wherein
Figure BDA0002340228580000026
Commonly referred to as P ═ XTX)-1XTFor hat matrix, note
Figure BDA0002340228580000031
As the fitting value of Y, the residual value is recorded as
Figure BDA0002340228580000032
Note that the sum of the squares of the residuals is:
Figure BDA0002340228580000033
variance of random error σ2Is estimated as
Figure BDA0002340228580000034
Further, the method for deleting curvature modal differences of a plurality of observation points, reconstructing a regression model, matrixing the regression model and then performing parameter estimation comprises the following steps:
the model after the ith data point is deleted is recorded as a data deletion model CDM expression:
yj＝Xj Tβ+εj，j＝1，2，…，n，j≠i；
wherein j ≠ i means that the model does not contain the ith data point;
the model matrix form is:
Y(i)＝X(i)β+ε(i)；
wherein Y (i), X (i), epsilon (i) represents a vector or a matrix of Y, X, epsilon and epsilon after deleting the corresponding ith component; the CDM model least squares regression coefficient at this time is:
Figure BDA0002340228580000035
regression residual sum of squares:
Figure BDA0002340228580000036
and random error variance estimation:
Figure BDA0002340228580000037
further, the method for statistically analyzing the difference between the regression coefficients before and after the observation point is deleted and determining whether the point is a damage in the structure includes the following steps:
the observation points were analyzed using the WK statistic (Welsch-Kul statics, Welsh-Kura statistic), defined as:
Figure BDA0002340228580000041
can also be written as
Figure BDA0002340228580000042
Wherein
Figure BDA0002340228580000043
piiIs a hat matrix P diagonal elements, and
Figure BDA0002340228580000044
obeying a t-distribution with a parameter of n-5;
given a significance level of α based on the WK distribution, the WK was obtainediConfidence intervals with confidence levels of 1- α are:
Figure BDA0002340228580000045
wherein t isα(n-5) is the upper α quantile of the t distribution;
thus, the ith data point { xi，yiThe judgment standard for the corresponding unit as a damaged unit is
Figure BDA0002340228580000046
Calculate i data points { xi，yi| WK of }iThe value of | and the threshold value
Figure BDA0002340228580000047
Make a comparison if
Figure BDA0002340228580000048
The ith cell is determined to be a defective cell.
The invention has the advantages that: the method provided by the invention can accurately find the structure damage position under the condition of larger environmental noise, has strong robustness and realizes data support for structure damage detection and health evaluation; the method can be applied to civil engineering such as bridges, high-rise buildings, hydraulic engineering and the like, and has wide application range; can be implemented in combination with programming, and the data processing is automatic and efficient.
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Fig. 1 is an aerial view of an experimental model of a high-piled wharf in the invention.
FIG. 2 is a cross-sectional view of an experimental model of a high-piled wharf according to the present invention.
Fig. 3 is a diagram of a sensor arrangement according to the present invention.
FIG. 4 is a graph of 10% damage behind the test point No. 5 in the present invention.
Fig. 5 is a diagram of frequency analysis of the wharf model of the present invention.
Fig. 6 is a curve of the difference in curvature modes in the present invention.
Fig. 7 shows the 10% damage identification process of the present invention.
Fig. 8 shows the 20% damage identification process of the present invention.
FIG. 9 is a table of experimental conditions in the present invention.
FIG. 10 is a schematic flow chart of the method of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
As shown in fig. 1 to 10, a structural damage recognition method based on a deletion model,
firstly, a high-pile wharf model is manufactured in a laboratory, the high-loading wharf model is shown in figures 1 and 2, 1 acceleration sensor is arranged on the second pile body on the left side of the front row from top to bottom every 0.01m, 10 acceleration sensors are arranged, the number of the acceleration sensors is 1,2, … … and 10 from top to bottom, the sensor arrangement diagram is shown in figure 3, and the vibration pickup direction of the sensors is vertical to the front edge direction of the wharf. The hammering time-course response before and after the pile body is damaged is collected to analyze the local vibration mode of the pile body, the damage is set to be that the pile foundation damage is simulated by adopting the cutting pile section to reduce the section inertia moment behind the No. 5 measuring point, the damage length is 0.01m as shown in figure 4, and the damage width and the test working condition are shown in the table 1.
The identification method specifically comprises the following steps:
the method comprises the following steps: obtaining the curvature modal difference between the current state and the intact state of the structure:
the mode analysis is carried out by using mature commercial software DHDAS after the test data are collected, fig. 5 is a natural frequency analysis chart of the structure, the graph shows that the order frequency of the structure 1 is 7.422Hz, the second order frequency is 20.703Hz, and the amplitude of the second order frequency corresponding to the vibration mode in the vibration pickup direction of the sensor is the largest, so that the second order vibration mode test data collected by the sensor have good signal-to-noise ratio, the second order local vibration mode of the pile body in the vibration pickup direction is analyzed through the test data to carry out damage identification, and the second order vibration modes of all working conditions are shown in table 2. A curvature mode difference curve is calculated from the mode shape as shown in fig. 6.
Step two: establishing a curvature mode difference polynomial regression model, and matrixing the regression model: let observation data be { xi， y i1,2, …, n. where x isiNumbering the measuring points, yiIs the curvature modal difference of the corresponding cell. Establishing a polynomial regression model:
Figure BDA0002340228580000061
vector of independent variables
Figure BDA0002340228580000062
Coefficient vector β ═ (β)0，β1，β2，β3)T. The model can be written in matrix form:
Y＝Xβ+ε.
wherein Y is (Y)1，y2，…，yn)T；ε＝(ε1，ε2，…εn)TIs a random error vector; x is an n X4 order matrix with the ith action
Figure BDA0002340228580000063
The regression model satisfies the regression model assumption: epsilon1，ε2，…εnObedience mean 0 and variance σ2Normal distributions independent of each other.
Thirdly, performing parameter estimation on the matrixed regression model, namely performing parameter estimation on the polynomial regression model by adopting a least square estimation method, namely searching for the estimation of the parameters β
Figure BDA0002340228580000064
Sum of squares of errors
Figure BDA0002340228580000065
To a minimum. Wherein
Figure BDA0002340228580000071
Commonly referred to as P ═ XTX)-1XTFor hat matrix, note
Figure BDA0002340228580000072
As the fitting value of Y, the residual value is recorded as
Figure BDA0002340228580000073
The sum of the squares of the residuals is
Figure BDA0002340228580000074
Variance of random error σ2Is estimated as
Figure BDA0002340228580000075
Step four: and deleting the curvature modal difference of a certain observation point, reestablishing a polynomial regression model, matrixing and carrying out parameter estimation. The model after the Deletion of the ith data point is recorded as a data Deletion model cdm (case Deletion model), and the expression is as follows:
yj＝Xj Tβ+εj，j＝1，2，…，n，j≠i.
wherein j ≠ i means that the model does not contain the ith data point matrix form as:
Y(i)＝X(i)β+ε(i).
where Y (i), X (i), ε (i) represents the vector or matrix after the removal of the corresponding i-th component { Y }, [ X ], { ε }. The CDM model least squares regression coefficient at this time is:
Figure BDA0002340228580000076
regression residual sum of squares:
Figure BDA0002340228580000077
and random error variance estimation:
Figure BDA0002340228580000078
the parameter estimation method is the same as the third step.
Step five: and analyzing the difference of regression coefficients before and after the observation point is deleted by using the WK statistic, and judging whether the point of the structure is damaged or not. The WK statistic is defined as:
Figure BDA0002340228580000081
can also be written as
Figure BDA0002340228580000082
Wherein
Figure BDA0002340228580000083
piiIs a hat matrix P diagonal elements, and
Figure BDA0002340228580000084
given a significance level of α based on the WK distribution, we obtained a WKiConfidence intervals with confidence levels of 1- α are:
Figure BDA0002340228580000085
wherein t isα/2(n-5) is the upper α/2 quantile of the t distribution;
thus, the ith data point { xi，yiThe judgment standard for the corresponding unit as a damaged unit is
Figure BDA0002340228580000086
That is, calculate i data points { xi，yi| WK of }iThe value of | and the threshold value
Figure BDA0002340228580000087
Make a comparison if
Figure BDA0002340228580000088
The ith cell is determined to be a defective cell.
Step six: judging whether the observation point is damaged: using the data deletion model for condition 1 (10% damage), the damage identification process is shown in fig. 7: and gradually deleting each unit to obtain MWK values of each unit after deletion, finding that the MWK value of the No. 5 unit is larger than the threshold value, and the MWK values of other units are smaller than the threshold value, so that the No. 5 unit can be determined as a damaged unit, which is consistent with the actual situation. Using a step-by-step data deletion model for condition 2 (20% damage), the damage identification process is shown in fig. 8: and gradually deleting each unit to obtain MWK values of each unit after deletion, finding that the MWK value of the No. 5 unit is larger than the threshold value, and the MWK values of other units are smaller than the threshold value, so that the No. 5 unit can be determined to be a damaged unit.
Based on the above, in a statistical sense, the damage identification is essentially to find out the abnormal points whose structural unit behaviors are different from the general rule. In actual engineering, a damaged area is local and small-range relative to the whole structure, so that the observed data features in the non-damaged area are dominant and dominant in the overall observed data, and the observed data features of the damaged area are different from those of the non-damaged observed area, so that the abnormal value which is found to be inconsistent with the whole data is the mathematical essence of structural damage identification. According to the curve characteristics of curvature mode difference before and after structural damage position damage, the curvature mode damage identification method based on the data deletion model, which is capable of automatically identifying and has high robustness, is established by deleting the influence of each observation point data on the overall curvature mode difference curve form. The damage experiment of the high-pile wharf model proves that the method has better applicability.
It will be appreciated by those skilled in the art that the invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The embodiments disclosed above are therefore to be considered in all respects as illustrative and not restrictive. All changes which come within the scope of or equivalence to the invention are intended to be embraced therein.

Claims (6)

1. A structural damage identification method based on a deletion model is characterized by comprising the following steps:
obtaining the curvature modal difference between the current state and the intact state of the structure;
constructing a regression model according to the curvature modal difference, and performing parameter estimation after matrixing the regression model;
deleting curvature modal differences of a plurality of observation points, rebuilding a regression model, matrixing the regression model and then performing parameter estimation;
and calculating the WK value of the observation point before and after deletion according to the parameter estimation result, and judging whether the point is the damage in the structure according to the WK value.
2. The structural damage identification method based on the deletion model according to claim 1, characterized in that: the method for acquiring the curvature modal difference comprises the following steps:
obtaining an initial curvature mode of the structure through a vibration test;
regularly observing the curvature mode of the current state;
and comparing the current curvature mode with the curvature mode in the intact state to obtain the curvature mode difference.
3. The structural damage identification method based on the deletion model according to claim 1, characterized in that: the method for constructing the regression model according to the curvature modal difference and matrixing the regression model comprises the following steps:
let observation data be { xi，yi}，i＝1，2，…，n；
Wherein xiNumbering the measuring points, yiIs the curvature mode difference of the corresponding unit;
establishing a regression model:
Figure FDA0002340228570000011
vector of independent variables
Figure FDA0002340228570000012
Coefficient vector β ═ (β)0，β1，β2，β3)T；
The model can be written in matrix form:
Y＝Xβ+ε；
wherein Y is (Y)1，y2，…，yn)T；ε＝(ε1，ε2，…εn)TThe random error vector satisfies the white noise condition; x is an n X4 order matrix with the ith action
Figure FDA0002340228570000028
4. The structural damage identification method based on the deletion model as claimed in claim 3, wherein: the method for parameter estimation of the matrixed regression model comprises the following steps:
finding an estimate of the parameter β using a least squares estimation method
Figure FDA0002340228570000021
The sum of the squares of the errors of the following equations:
Figure FDA0002340228570000022
the minimum is reached;
to obtain
Figure FDA0002340228570000023
The term P ═ XTX)-1XTFor hat matrix, note
Figure FDA0002340228570000024
As the fitting value of Y, the residual value is recorded as
Figure FDA0002340228570000025
Note that the sum of the squares of the residuals is:
Figure FDA0002340228570000026
variance of random error σ2Is estimated as
Figure FDA0002340228570000027
5. The structural damage identification method based on the deletion model as claimed in claim 4, wherein: the method for deleting curvature modal differences of a plurality of observation points, reconstructing a regression model, matrixing the regression model and then estimating parameters comprises the following steps:
and marking the model after the ith data point is deleted as a data deletion model, wherein the expression is as follows:
yj＝Xj Tβ+εj，j＝1，2，…，n，j≠i；
wherein j ≠ i means that the model does not contain the ith data point;
the model matrix form is:
Y(i)＝X(i)β+ε(i)；
wherein Y (i), X (i), epsilon (i) represents a vector or a matrix of Y, X, epsilon and epsilon after deleting the corresponding ith component; the least squares regression coefficient of the data deletion model at this time is:
Figure FDA0002340228570000031
regression residual sum of squares:
Figure FDA0002340228570000032
and random error variance estimation:
Figure FDA0002340228570000033
6. the structural damage identification method based on the deletion model as claimed in claim 5, wherein: the method for calculating the WK value before and after deletion of the observation point according to the parameter estimation result and judging whether the point is a damage in the structure according to the WK value comprises the following steps:
analyzing observation points by adopting WK statistics, wherein the observation points are defined as:
Figure FDA0002340228570000034
can also be written as
Figure FDA0002340228570000035
Wherein
Figure FDA0002340228570000036
piiIs a hat matrix P diagonal elements, and
Figure FDA0002340228570000037
obeying a t-distribution with a parameter of n-5;
given a significance level of α based on the WK distribution, the WK was obtainediConfidence intervals with confidence levels of 1- α are:
Figure FDA0002340228570000041
wherein t isα(n-5) is the upper α quantile of the t distribution;
thus, the ith data point { xi，yiThe judgment standard for the corresponding unit as a damaged unit is as follows:
Figure FDA0002340228570000042
calculate i data points { xi，yi| WK of }iThe value of | and the threshold value
Figure FDA0002340228570000043
Make a comparison if
Figure FDA0002340228570000044
The ith cell is determined to be a defective cell.
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Citations (4)

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Publication number Priority date Publication date Assignee Title
CN105064420A (en) * 2015-08-06 2015-11-18 交通运输部天津水运工程科学研究所 High-pile wharf foundation pile damage diagnosis method based on structural residual modal force
CN106897543A (en) * 2017-04-25 2017-06-27 湘潭大学 The girder construction damnification recognition method of On Modal Flexibility Curvature matrix norm
CN109543303A (en) * 2018-11-22 2019-03-29 华北水利水电大学 A method of the Damage Assessment Method to be perturbed based on class curvature of the flexibility difference matrix and frequency
CN110455476A (en) * 2019-07-29 2019-11-15 河海大学 A kind of multidimensional dynamical dactylogram damnification recognition method based on MCD abnormal point checking method

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105064420A (en) * 2015-08-06 2015-11-18 交通运输部天津水运工程科学研究所 High-pile wharf foundation pile damage diagnosis method based on structural residual modal force
CN106897543A (en) * 2017-04-25 2017-06-27 湘潭大学 The girder construction damnification recognition method of On Modal Flexibility Curvature matrix norm
CN109543303A (en) * 2018-11-22 2019-03-29 华北水利水电大学 A method of the Damage Assessment Method to be perturbed based on class curvature of the flexibility difference matrix and frequency
CN110455476A (en) * 2019-07-29 2019-11-15 河海大学 A kind of multidimensional dynamical dactylogram damnification recognition method based on MCD abnormal point checking method

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