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CN111723427B - Bridge structure damage positioning method based on recursive feature decomposition - Google Patents

Bridge structure damage positioning method based on recursive feature decomposition Download PDF

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CN111723427B
CN111723427B CN202010584428.0A CN202010584428A CN111723427B CN 111723427 B CN111723427 B CN 111723427B CN 202010584428 A CN202010584428 A CN 202010584428A CN 111723427 B CN111723427 B CN 111723427B
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聂振华
谢永康
马宏伟
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Jinan University
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Abstract

The invention discloses a method for positioning damage of a bridge structure based on recursive feature decomposition, which comprises the following steps: arranging two vertical displacement sensors at any position on the bridge, and measuring the vertical displacement dynamic response of the bridge; enabling the vehicle to pass through the bridge at a constant speed, and constructing an initial data matrix X by using the collected signals with the first L lengths0(ii) a To X0The normalized initial data matrix with the column mean value of 0 and the column standard deviation of 1 is obtained by normalizing each column of data
Figure DDA0002554083160000011
Computing
Figure DDA0002554083160000012
Of the covariance matrix R0(ii) a Sequentially inputting the displacement response x at the ith momenti＝[x1i x2i]Obtaining the covariance matrix R at the moment by a recursive methodi(ii) a Covariance matrix R for the ith timeiCarrying out feature decomposition and extracting feature vectors; defining a damage index RDC (i) at the ith moment; and after all the measured data are calculated in a recursion mode, obtaining an RDC (radio data center) (i) time sequence, determining the time point when the vehicle passes through the damage position of the bridge according to the mutation position of the RDC (i) curve, and multiplying the determined damage time point by the moving speed of the vehicle to calculate the damage position of the bridge.

Description

Bridge structure damage positioning method based on recursive feature decomposition
Technical Field
The invention relates to the technical field of structural safety monitoring, in particular to a bridge structure damage positioning method based on recursive feature decomposition.
Background
In the traditional bridge damage detection work, a large number of sensors are generally arranged on a bridge, signals are continuously acquired in the bridge operation process, and the signals are compared with health reference data to monitor the structural health condition. The method brings many problems, for example, the excessive number of sensors generates huge engineering cost, mass data is difficult to store and process, and health data of a part of bridges which are built for a long time are missing and cannot provide reference. Therefore, a method for positioning damage to a bridge structure based on recursive feature decomposition is urgently needed. The method is based on a data driving principle, does not need reference data in a bridge health state, and can realize bridge damage positioning only by two vertical displacement sensors on the bridge.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a method for positioning damage of a bridge structure based on recursive feature decomposition.
The purpose of the invention can be achieved by adopting the following technical scheme:
a bridge structure damage positioning method based on recursive feature decomposition comprises the following steps:
s1, arranging two vertical displacement sensors at any position on the bridge, and measuring the vertical displacement dynamic response of the bridge;
s2, enabling the vehicle to pass through the bridge at a constant speed, and constructing an initial data matrix X from the collected signals with the first L lengths0：
Figure BDA0002554083140000021
Wherein, X0Each column of (a) represents a signal measured by a sensor;
s3, for X0The normalized initial data matrix with the column mean value of 0 and the column standard deviation of 1 is obtained by normalizing each column of data
Figure BDA0002554083140000022
Figure BDA0002554083140000023
In the formula, e, m0、Σ0Coefficient vector, initial mean vector and initial standard deviation matrix, respectively, are obtained by the following formula:
Figure BDA0002554083140000024
in the formula, σ10、σ20Respectively representing the standard deviation of the 1 st and 2 nd sensor initial data column vectors;
s4, calculating a normalized initial data matrix
Figure BDA0002554083140000025
Of the covariance matrix R0I.e. initial covariance matrix:
Figure BDA0002554083140000026
s5, continuously and sequentially inputting the displacement response x at the ith momenti＝[x1i x2i]Wherein x is1i、x2iRespectively measuring the displacement response of the 1 st sensor and the 2 nd sensor at the ith moment, wherein i is L +1, L +2, …, N and N is the total length of the measured data of the vehicle passing through the full bridge, and obtaining the covariance matrix R at the ith moment by a recursive methodiThe recursive formula is as follows:
Figure BDA0002554083140000031
in the formula,. DELTA.miIs a vector of the mean difference at the ith time,
Figure BDA0002554083140000032
for the normalized displacement response vector at time i, it is iteratively found by:
Figure BDA0002554083140000033
Δmi＝mi-mi-1
Figure BDA0002554083140000034
wherein
Figure BDA0002554083140000035
And (3) iteratively solving the standard deviation matrix at the ith moment by the following formula:
Figure BDA0002554083140000036
Figure BDA0002554083140000037
wherein, Δ mi(1)，Δmi(2) Mean difference, σ, of responses measured by the 1 st and 2 nd sensors, respectively, at the i-th time1i，σ2iStandard deviation, σ, of the signals measured by the 1 st and 2 nd sensors, respectively, at the i-th time1(i-1)，σ2(i-1)The standard deviations of the signals measured by the 1 st and 2 nd sensors at the i-1 st moment,
Figure BDA0002554083140000038
s6 covariance matrix R at i-th timeiCarrying out eigenvalue decomposition and extracting eigenvectors:
Figure BDA0002554083140000039
in the formula (I), the compound is shown in the specification,
Figure BDA00025540831400000310
λ1i、λ2irespectively a first eigenvector, a second eigenvector, a first eigenvalue and a second eigenvalue at the ith moment;
s7, the damage index at the ith time is defined as recursive offset curvature rdc (i), and the damage index rdc (i) is defined as follows:
Figure BDA0002554083140000041
wherein RD (i) is determined by the following formula:
Figure BDA0002554083140000042
wherein X (i) and X (i-1) respectively represent displacement data matrixes at the i-th time and the i-1-th time,
Figure BDA0002554083140000043
Figure BDA0002554083140000044
respectively a first eigenvector and a second eigenvector at the i-1 moment;
and S8, after all the measured data are recursively calculated, obtaining a recursive offset curvature RDC (i) time sequence, determining the time point when the vehicle passes through the damage position of the bridge according to the abrupt change position of the curve of the recursive offset curvature RDC (i), and multiplying the time point when the damage position of the bridge is determined by the moving speed of the vehicle to calculate the damage position of the bridge.
Further, in step S2, the parameter L is determined as follows:
L＝fs
wherein f issIs the signal sampling frequency.
Compared with the prior art, the invention has the following advantages and effects:
1) the invention is a pure data driving method, does not need to establish a finite element model, and overcomes the problems of complex structure and difficulty in establishing an accurate finite element model in the actual engineering.
2) The method can be used for carrying out damage positioning by directly utilizing the current operation state of the bridge without structural health reference data. The traditional method generally needs structural health data as reference comparison, but the problem of health data loss exists in a part of bridges which are long in construction time, and the method can effectively solve the problem.
3) The method can realize the bridge damage positioning by only installing two sensors on the bridge, thereby avoiding the process of arranging a large number of sensors on the bridge in the traditional monitoring method, greatly reducing the number of the monitoring sensors and the storage amount of the monitoring data, and effectively solving the problem that the structural damage detection needs a large number of sensors and mass data is difficult to process.
Drawings
FIG. 1 is a flowchart of a method for positioning damage to a bridge structure based on recursive feature decomposition according to the present invention;
FIG. 2 is a simplified diagram of a simple beam bridge model in an embodiment of the present invention;
FIG. 3 is a RDC (i) graph of a 10% beam bridge damage using sensor 1 and sensor 2 according to an embodiment of the present invention;
FIG. 4 is a graph of RDC (i) for a 30% beam bridge damage using sensor 1 and sensor 2 in an embodiment of the present invention;
FIG. 5 is a RDC (i) graph of a 10% beam bridge damage using sensor 1 and sensor 3 in an embodiment of the present invention;
FIG. 6 is a RDC (i) graph of a 30% beam bridge damage using sensor 1 and sensor 3 in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
Detailed diagram 2 of the beam bridge model used in this embodiment, the length l of the model beam is 20m, and the sampling frequency fsIs 200 Hz. To illustrate the effectiveness of the method, two damage conditions, 10% and 30%, were set using a deletion unit at 0.4l of the beam length. The specific implementation process is as follows:
s1, as shown in figure 2, arranging a vertical displacement sensor 1 and a sensor 2 at the position 2l/8 and the position 3l/8 of the bridge respectively to measure the vertical displacement response of the bridge. In order to illustrate the effectiveness of the sensor in the method, the vertical displacement sensor 3 is arranged at the 6l/8 position of the bridge far away from damage, and the effect is verified by adopting two pairing modes of the sensor 1 and the sensor 2 and the sensor 1 and the sensor 3;
s2, enabling the vehicle (simplified into a moving mass) to pass through the bridge at a constant speed of v-0.2 m/S, and constructing an initial data matrix X from the collected signals with the first L lengths0Comprises the following steps:
Figure BDA0002554083140000061
wherein X0Each column of (a) represents a signal measured by one sensor, and the parameter L is determined as follows:
L＝fs＝200Hz
wherein f issIs the signal sampling frequency;
s3, in order to eliminate the influence of the dimension, normalizing each column of data so that the column mean is 0 and the column standard deviation is 1:
Figure BDA0002554083140000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002554083140000063
to normalize the initial data matrix, e, m0、Σ0The coefficient vector, the initial mean vector and the initial standard deviation matrix are obtained by the following formula:
Figure BDA0002554083140000064
in the formula, σ10，σ20Representing the 1 st and 2 nd initial sensor data columnsStandard deviation;
s4, calculating a normalized initial data matrix
Figure BDA0002554083140000065
Of the covariance matrix R0I.e. initial covariance matrix:
Figure BDA0002554083140000066
s5, continuously and sequentially inputting the displacement x at the ith momenti＝[x1i x2i](i＝L+1,L+2,…,N，N＝lfs20000 is the total data length), the covariance matrix R at the time i is obtained by the recursive methodiThe recursive calculation method is as follows:
Figure BDA0002554083140000071
in the formula,. DELTA.miIs a vector of the mean difference at the ith time,
Figure BDA0002554083140000072
the normalized displacement vector for the ith time instant can be iteratively calculated by:
Figure BDA0002554083140000073
Δmi＝mi-mi-1
Figure BDA0002554083140000074
wherein
Figure BDA0002554083140000075
And (3) iteratively solving the standard deviation matrix at the ith moment by the following formula:
Figure BDA0002554083140000076
Figure BDA0002554083140000077
wherein, Δ mi(1)，Δmi(2) The mean differences of the responses measured by the 1 st and 2 nd sensors at time i respectively,
Figure BDA0002554083140000078
s6 covariance matrix R at i-th timeiCarrying out eigenvalue decomposition and extracting eigenvectors:
Figure BDA0002554083140000079
in the formula (I), the compound is shown in the specification,
Figure BDA00025540831400000710
λ1i、λ2irespectively a first eigenvector, a second eigenvector, a first eigenvalue and a second eigenvalue at the ith moment.
S7, the damage index at the ith time is defined as recursive offset curvature rdc (i), and the damage index rdc (i) is defined as follows:
Figure BDA0002554083140000081
wherein RD (i) is determined by the following formula:
Figure BDA0002554083140000082
wherein x (i) represents a displacement data matrix at the ith time;
Figure BDA0002554083140000083
first feature vector and second feature at the i-1 th time point respectivelyA eigenvector;
and S8, obtaining an RDC (RDC) (i) time sequence after all the measured data are calculated in a recursion mode, and determining the time point of the vehicle passing through the damage position of the bridge according to the mutation position of the RDC (i) curve. If the bridge is damaged, the RDC (i) curve is subjected to mutation when the vehicle passes through the damaged position, and the RDC (i) curve is not subjected to mutation under the healthy condition. The damage time corresponding to the mutation position under the working conditions of 10% damage and 30% damage is approximately t-8000/200 Hz-40 s.
And multiplying the determined damage time point by the moving speed of the vehicle to calculate the damage position of the bridge to be approximately 40 s-0.2 m/s-8 m, namely approximately at the position of the bridge length of 0.4 l. Fig. 3 and 4 are rdc (i) graphs of sensor 1 and sensor 2, and it can be seen from the graphs that, under both damage conditions, the curves suddenly change at 0.4l (damage position), and under healthy conditions, the curves do not have the phenomenon. This shows that the method can achieve lesion localization with dual sensors without reference data. Fig. 5-6 are rdc (i) graphs of sensor 1 and sensor 3, which show that the above effects are also obtained, and further show that the method is not limited by the arrangement position of the sensors.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (2)

1. A bridge structure damage positioning method based on recursive feature decomposition is characterized by comprising the following steps:
s1, arranging two vertical displacement sensors at any position on the bridge, and measuring the vertical displacement dynamic response of the bridge;
s2, enabling the vehicle to pass through the bridge at a constant speed, and constructing an initial data matrix X from the collected signals with the first L lengths0：
Figure FDA0002554083130000011
Wherein X0Each column of (a) represents a signal measured by a sensor;
s3, for X0The normalized initial data matrix with the column mean value of 0 and the column standard deviation of 1 is obtained by normalizing each column of data
Figure FDA0002554083130000012
Figure FDA0002554083130000013
In the formula, e, m0、Σ0Coefficient vector, initial mean vector and initial standard deviation matrix, respectively, are obtained by the following formula:
Figure FDA0002554083130000014
in the formula, σ10、σ20Respectively representing the standard deviation of the 1 st and 2 nd sensor initial data column vectors;
s4, calculating a normalized initial data matrix
Figure FDA0002554083130000015
Of the covariance matrix R0I.e. initial covariance matrix:
Figure FDA0002554083130000021
s5, continuously and sequentially inputting the displacement response x at the ith momenti＝[x1i x2i]Wherein x is1i、x2iThe displacement response measured by the 1 st and 2 nd sensors at the i-th moment, i ═ L +1, L +2, …, N, N is the total length of data measured by the vehicle passing through the full bridge, and the data are processed by recursionThe method obtains the covariance matrix R of the ith momentiThe recursive formula is as follows:
Figure FDA0002554083130000022
in the formula,. DELTA.miIs a vector of the mean difference at the ith time,
Figure FDA0002554083130000023
for the normalized displacement response vector at time i, it is iteratively found by:
Figure FDA0002554083130000024
Δmi＝mi-mi-1
Figure FDA0002554083130000025
wherein
Figure FDA0002554083130000026
And (3) iteratively solving the standard deviation matrix at the ith moment by the following formula:
Figure FDA0002554083130000027
Figure FDA0002554083130000028
wherein, Δ mi(1)，Δmi(2) Mean difference, σ, of responses measured by the 1 st and 2 nd sensors, respectively, at the i-th time1i，σ2iStandard deviation, σ, of the signals measured by the 1 st and 2 nd sensors, respectively, at the i-th time1(i-1)，σ2(i-1)The standard deviations of the signals measured by the 1 st and 2 nd sensors at the i-1 st moment,
Figure FDA0002554083130000029
s6 covariance matrix R at i-th timeiCarrying out eigenvalue decomposition and extracting eigenvectors:
Figure FDA0002554083130000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002554083130000032
λ1i、λ2irespectively a first eigenvector, a second eigenvector, a first eigenvalue and a second eigenvalue at the ith moment;
s7, the damage index at the ith time is defined as recursive offset curvature rdc (i), and the damage index rdc (i) is defined as follows:
Figure FDA0002554083130000033
wherein RD (i) is determined by the following formula:
Figure FDA0002554083130000034
wherein X (i) and X (i-1) respectively represent displacement data matrixes at the i-th time and the i-1-th time,
Figure FDA0002554083130000035
Figure FDA0002554083130000036
respectively a first eigenvector and a second eigenvector at the i-1 moment;
and S8, after all the measured data are recursively calculated, obtaining a recursive offset curvature RDC (i) time sequence, determining the time point when the vehicle passes through the damage position of the bridge according to the abrupt change position of the curve of the recursive offset curvature RDC (i), and multiplying the time point when the damage position of the bridge is determined by the moving speed of the vehicle to calculate the damage position of the bridge.
2. The method for positioning damage to a bridge structure based on recursive feature decomposition of claim 1, wherein in step S2, the parameter L is determined as follows:
L＝fs
wherein f issIs the signal sampling frequency.
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