CN112229587A - Method for indirectly measuring dynamic deflection of high-speed rail bridge based on inclinometer - Google Patents

Method for indirectly measuring dynamic deflection of high-speed rail bridge based on inclinometer Download PDF

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CN112229587A
CN112229587A CN202011079101.4A CN202011079101A CN112229587A CN 112229587 A CN112229587 A CN 112229587A CN 202011079101 A CN202011079101 A CN 202011079101A CN 112229587 A CN112229587 A CN 112229587A
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deflection
inclinometer
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speed railway
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王川
李欣澄
万闯
梅婷
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Harbin Institute of Technology
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Abstract

The invention provides a method for indirectly measuring dynamic deflection of a high-speed railway bridge based on an inclinometer, which utilizes the differential relation of deflection lines of the high-speed railway bridge under small deformation and a new interpolation algorithm and utilizes the monitoring information of an inclinometer sensor of the high-speed railway bridge to realize real-time monitoring of the dynamic deflection of the bridge. And the effectiveness of the segmented cubic spline interpolation method in measuring the dynamic deflection of the high-speed rail bridge is proved by combining the corner-deflection data of the standard beam of the salt line high-speed rail and carrying out error analysis through an algorithm. The method is an indirect and effective method for monitoring the dynamic deflection of the bridge, is economic and efficient, overcomes the defect that the traditional method such as a dial indicator, a pull rod displacement sensor, a laser interferometer method and the like are directly used for measuring the deflection of the bridge, is suitable for measuring the deflection of the high-speed railway bridge under the complex geological condition, and provides deflection data for a high-speed railway bridge health detection system.

Description

Method for indirectly measuring dynamic deflection of high-speed rail bridge based on inclinometer
Technical Field
The invention belongs to the field of bridge engineering health monitoring, and particularly relates to a method for indirectly measuring dynamic deflection of a high-speed rail bridge based on an inclinometer.
Background
Until now, no general method exists for monitoring the dynamic deflection of the bridge, for example, a stay wire type displacement meter is limited to the bridge with water under the bridge or with higher clearance under the bridge for measuring the dynamic deflection; the laser method can only measure the bridge closer to the bridge head; the test precision of the GPS measurement method can only reach the centimeter level at most and cannot meet the requirement of the test precision.
Therefore, how to test the dynamic deflection of the high-speed railway bridge under complex geological conditions such as crossing a large river is a difficult problem to be solved, the inclinometer sensor has the characteristics of high precision, small volume, convenient arrangement, no need of a static reference point and the like, the problem that the bridge deflection measurement process is limited by environment, instrument precision and the like can be solved, and the measurement result of the high-speed railway bridge deflection is directly influenced by the quality of an algorithm for calculating the deflection, so the invention provides a novel method for indirectly measuring the dynamic deflection of the high-speed railway bridge by using a bridge corner, namely a segmented cubic spline interpolation method.
Disclosure of Invention
The invention aims to solve the problem that a high-speed rail bridge is limited by environment, instrument precision and the like in the deflection measurement process, and provides a method for indirectly measuring the dynamic deflection of the high-speed rail bridge based on an inclinometer.
The purpose of the invention is realized by the following technical scheme:
a method for indirectly measuring dynamic deflection of a high-speed rail bridge based on an inclinometer comprises the following steps:
the method comprises the following steps: arranging m rows of n rows of inclinometer sensors according to an actual high-speed rail bridge, and extracting an original corner signal;
step two: filtering out interference signals of the original corner signals through a Butterworth low-pass filter to obtain corner data of the high-speed railway bridge;
step three: and taking the arrangement positions of the inclinometer sensors and the extracted corner data as input, calculating the deflection curve between every two inclinometer sensors by a segmented cubic spline interpolation algorithm, and drawing the integral deflection curve of the high-speed rail bridge.
Compared with the prior art, the invention has the following advantages:
according to the traditional measuring method, a corner curve is fitted firstly, and then the corner curve is integrated to obtain a deflection curve of the bridge, the characteristic that the high-speed railway beam is a simply supported beam is not fully considered and utilized, and the effect is poor in the practical application process.
The invention directly carries out segmented cubic spline interpolation on a deflection curve, then utilizes the differential relation between corners and deflection to convert the beam deflection interpolation into the beam deflection interpolation, and because the interpolation algorithm is lack of boundary conditions, a high-speed railway bridge is a simply supported beam, and the deflection value at a support is zero, the method not only utilizes the beam deflection differential relation between corners and deflection, but also considers the structural characteristics of the actual high-speed railway bridge and determines the boundary conditions of the interpolation algorithm, so that the interpolation algorithm has good application effect theoretically, the invention calculates the deflection curve of the high-speed railway bridge by a novel segmented cubic spline interpolation algorithm based on the bridge corner signals measured by an inclinometer, can achieve the effect of monitoring the dynamic deflection of the high-speed railway bridge in real time on line, is economic and efficient, and makes up the traditional method such as directly using a dial indicator, the defects that instruments such as a pull rod displacement sensor, a laser interferometer method and the like are used for measuring the bridge deflection are overcome, the method is suitable for measuring the high-speed railway bridge deflection under the complex geological condition, and powerful support is provided for a health detection system of a high-speed railway bridge.
Drawings
FIG. 1: the stress of the simply supported beam is shown schematically;
FIG. 2: a schematic diagram of a piecewise cubic spline interpolation algorithm;
FIG. 3: a schematic diagram of the layout of the inclinometer;
FIG. 4: (a) the signal is the original corner signal of the inclinometer, (b) the inclinometer signal is subjected to noise removal by a Butterworth low-pass filter;
FIG. 5: the method and the dial indicator (displacement meter) respectively measure the dynamic deflection of the high-speed rail bridge under different working conditions; (a) the actual measurement result is under the working condition of 0.80 grade; (b) the actual measurement result is under the working condition of 1.05 grade; (c) the actual measurement result is under the working condition of 1.10 level; (d) the measured result is the measured result under the working condition of 1.20 grades.
Detailed Description
The technical solutions of the present invention are further described below with reference to fig. 1 to 5, but not limited thereto, and modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the scope of the technical solutions of the present invention.
As shown in figure 1, for a high-speed railway bridge with small deflection, the bending rigidity is EI, a tiny unit body dx on the bridge is taken, and the bridge is subjected to uniform load q and concentrated force FpAnd a concentration couple MiUnder the action of the pressure, the sum of the bending moments is M (x),
the deflection generated by the high-speed railway bridge is f, and the high-speed railway bridge is formed by a small-deformation deflection line differential equation (1) and a deflection f-corner theta differential relation (2):
Figure BDA0002718081700000021
Figure BDA0002718081700000031
Figure BDA0002718081700000032
wherein, C1And C2Is a constant term;
it can be concluded that, in general, the high-speed railway bridge deflection f is a polynomial function (3) not exceeding 4 times, and the function itself is continuous, and the first derivative (corner) and the second derivative (curvature) are also smooth and continuous, based on which, assuming that k inclinometers are arranged on a certain span of the bridge, as shown in fig. 2, a local coordinate system is established with one end point of the beam as the origin, and in the interval [ x [ ]i,xi+1]The deflection curve ofi(x) The true deflection of the point to be measured is f1,f2,…,fkThen, it can be set as follows:
Figure BDA0002718081700000033
wherein c isi，diFor the adjustment coefficients of the interpolation function, the curve continuity condition is used to determine
Recording:
hi＝xi+1-xiaccording to y'i(xi)＝θi,y'i(xi+1)＝θi+1,y"i(xi+1)＝y"i+1(xi+1)
The derivation is as follows:
Figure BDA0002718081700000034
Figure BDA0002718081700000035
the reaction is not allowed to proceed:
Figure BDA0002718081700000036
then it is possible to obtain:
Figure BDA0002718081700000041
interpolation boundary conditions: f. of1＝DA,fk＝DB,DA,DBIn the invention, the displacement of a boundary support is taken for interpolating the deflection of the curve boundary, the high-speed rail standard beam is a simply supported beam, and the displacement at the boundary support is zero, namely DA＝D B0, from inclinometer data θiThe deflection value f of each measuring point can be obtained through the matrix equationiThe curve y of each section can be obtained by substituting the interpolation expression into the interpolation expressioni(x) And obtaining the calculated deflection curve.
Detailed description of the invention
A method for indirectly measuring dynamic deflection of a high-speed rail bridge based on an inclinometer comprises the following steps:
the method comprises the following steps: the invention discloses a layout of inclinometer sensors, wherein m rows and n columns of sensors are arranged on a standard 32-meter high-speed rail beam, the inclinometer sensors are arranged in 3 rows and 9 columns in each row, a corner signal is extracted, and an interference signal is filtered out through a Butterworth low-pass filter to obtain corner data response of the beam.
Step two: taking the extracted corner data as input, calculating a deflection curve between every two inclinometers through a cubic spline interpolation algorithm, and drawing the deflection curve of the whole beam;
step three: and (4) processing the actual deflection value obtained by measuring the dial indicator through the filter in the step one to obtain the actual vertical displacement response of the beam.
The invention adopts segmented cubic spline interpolation for measuring the deflection of the high-speed railway bridge, utilizes the characteristic that the high-speed railway bridge can be regarded as a simply supported beam with zero deflection value at a support, solves the problem of boundary conditions of an interpolation expression, sets a curve expression on each segment according to the characteristic that the deflection curve of the high-speed railway beam is a polynomial not more than fourth degree, and determines the boundary conditions of the interpolation by utilizing the structural characteristic that the deflection at the support of the simply supported beam is zero, thereby forming a new deflection measuring algorithm.
In actual tests, the arrangement of the inclinometer is optimized through a test on the standard high-speed rail beam with the salt through line of 32 meters, the arrangement is divided into 3 rows and 9 columns, the problem of transverse unbalance loading caused by too wide bridge deck is solved, effective test data are obtained, and the effectiveness of an algorithm is verified.
When the inclinometer sensors are arranged, if odd number of sensors are uniformly arranged, the coefficient betaiWhen the inclinometer sensors are arranged, an arrangement mode of equal distance and odd number should be avoided, and besides, the arrangement scheme of the measuring points, such as arrangement schemes of equal distance and even number of measuring points, unequal distance odd number of measuring points, unequal distance and even number of measuring points, and the like, the equations are all solvable.
Example 1:
the effectiveness of the algorithm is verified through a salt-flux high-speed rail 32-meter standard beam, an inclinometer network is arranged in the high-speed rail bridge and consists of 27 QY-type inclinometers, and the corner history of the high-speed rail bridge can be monitored in real time.
Step 1: the algorithm of the invention utilizes the sensor information of the inclinometers of a plurality of channels to identify the corner of the high-speed rail bridge, adopts the QY type inclinometer, and the inclinometers are divided into 3 rows which are arranged at the upper part, the middle part and the lower part, and 9 inclinometers are arranged at equal intervals in each row (figure 3).
Step 2: designing Butterworth low-pass filter, adjusting cut-off frequency, filtering noise interference signal, extracting inclination angle signal (fig. 4)
And step 3: the arrangement position and the corner data of the inclinometer are input into a segmented cubic spline interpolation algorithm in response, a deflection value is calculated, an interpolated deflection curve is drawn, the interpolated deflection curve is compared with the deflection value actually measured by a dial indicator, and the effectiveness of the algorithm under different working conditions is verified (fig. 5 (a-d)).
The deflection curve measured by the method is well matched with the deflection measured by an actual dial indicator, so that the algorithm provided by the invention has a good effect, the relative error is within an allowable range (within 5%), and the method can be applied to the measurement of bridge deflection in a high-speed railway bridge health monitoring system.

Claims (3)

1. A method for indirectly measuring dynamic deflection of a high-speed rail bridge based on an inclinometer is characterized by comprising the following steps:
the method comprises the following steps: arranging m rows of n rows of inclinometer sensors according to an actual high-speed rail bridge, and extracting an original corner signal;
step two: filtering out interference signals of the original corner signals through a Butterworth low-pass filter to obtain corner data of the high-speed railway bridge;
step three: and taking the arrangement positions of the inclinometer sensors and the extracted corner data as input, calculating the deflection curve between every two inclinometer sensors by a segmented cubic spline interpolation algorithm, and drawing the integral deflection curve of the high-speed rail bridge.
2. The base of claim 1The method for indirectly measuring the dynamic deflection of the high-speed rail bridge by using the inclinometer is characterized by comprising the following steps of: in the third step, suppose that k inclinometer sensors are arranged on a certain span of the high-speed rail bridge, a local coordinate system is established by taking one end point of the high-speed rail bridge as an origin, and the local coordinate system is arranged in an interval [ x ]i,xi+1]The deflection curve ofi(x) The true deflection of the point to be measured is f1,f2,…,fkThen, it can be set as follows:
Figure FDA0002718081690000011
recording: h isi＝xi+1-xiAccording to y'i(xi)＝θi,y′i(xi+1)＝θi+1,y″i(xi+1)＝y″i+1(xi+1) The derivation is:
Figure FDA0002718081690000012
Figure FDA0002718081690000013
order:
Figure FDA0002718081690000014
then a matrix equation can be obtained:
Figure FDA0002718081690000021
interpolation boundary conditions: f. of1＝DA,fk＝DB,DA,DBFor the deflection of the interpolation curve boundary, the high-speed rail standard beam is a simply supported beam, and the displacement at the boundary support is zero, i.e.DA＝DB0, from inclinometer angle data θiThe deflection value f of each measuring point can be obtained through the matrix equationiThe curve y of each section can be obtained by substituting the interpolation expression into the interpolation expressioni(x) And obtaining the calculated deflection curve.
3. The method for indirectly measuring the dynamic deflection of the high-speed railway bridge based on the inclinometer as claimed in claim 1, is characterized in that: in the first step, an equidistant even number of inclinometer sensors, an unequal distance odd number of inclinometer sensors or an unequal distance even number of inclinometer sensors are distributed.
CN202011079101.4A 2020-10-10 2020-10-10 Method for indirectly measuring dynamic deflection of high-speed rail bridge based on inclinometer Pending CN112229587A (en)

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
CN112883480A (en) * 2021-04-09 2021-06-01 云南大学 Bridge load test evaluation method by utilizing dip angle and displacement combined test
CN113221354A (en) * 2021-05-11 2021-08-06 西安电子科技大学 Pipeline bending deformation fitting algorithm
CN113239481A (en) * 2021-04-22 2021-08-10 中国铁路设计集团有限公司 Dynamic deflection monitoring method for standard simply supported beam of 32-meter high-speed rail
CN113283130A (en) * 2021-04-21 2021-08-20 中国铁路设计集团有限公司 Method for monitoring dynamic deflection of standard beam of 32 meters of high-speed railway based on strain mode
CN113408023A (en) * 2021-04-26 2021-09-17 深圳华星智感科技有限公司 Beam and plate vertical displacement calculation method based on corner
CN114168906A (en) * 2022-02-14 2022-03-11 威海市房地产测绘中心有限公司 Mapping geographic information data acquisition system based on cloud computing

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Cited By (9)

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Publication number Priority date Publication date Assignee Title
CN112883480A (en) * 2021-04-09 2021-06-01 云南大学 Bridge load test evaluation method by utilizing dip angle and displacement combined test
CN113283130A (en) * 2021-04-21 2021-08-20 中国铁路设计集团有限公司 Method for monitoring dynamic deflection of standard beam of 32 meters of high-speed railway based on strain mode
CN113283130B (en) * 2021-04-21 2022-04-15 中国铁路设计集团有限公司 Method for monitoring dynamic deflection of standard beam of 32 meters of high-speed railway based on strain mode
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CN113239481B (en) * 2021-04-22 2022-03-08 中国铁路设计集团有限公司 Dynamic deflection monitoring method for standard simply supported beam of 32-meter high-speed rail
CN113408023A (en) * 2021-04-26 2021-09-17 深圳华星智感科技有限公司 Beam and plate vertical displacement calculation method based on corner
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CN113221354A (en) * 2021-05-11 2021-08-06 西安电子科技大学 Pipeline bending deformation fitting algorithm
CN114168906A (en) * 2022-02-14 2022-03-11 威海市房地产测绘中心有限公司 Mapping geographic information data acquisition system based on cloud computing

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