CN112229587A - A method for indirect measurement of dynamic deflection of high-speed railway bridges based on inclinometers - Google Patents

A method for indirect measurement of dynamic deflection of high-speed railway bridges based on inclinometers 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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王川
李欣澄
万闯
梅婷
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Harbin Institute of Technology Shenzhen
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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)

1.一种基于倾角仪间接测量高铁桥梁动挠度的方法，其特征在于，所述方法包括以下步骤：1. a method for indirectly measuring the dynamic deflection of a high-speed rail bridge based on an inclinometer, is characterized in that, the method comprises the following steps: 步骤一：根据实际高铁桥梁布设m排n列倾角仪传感器，提取原始转角信号；Step 1: According to the actual high-speed railway bridge, m rows and n columns of inclinometer sensors are arranged to extract the original rotation angle signal; 步骤二：通过巴特沃斯低通滤波器滤去原始转角信号的干扰信号，得到高铁桥梁的转角数据；Step 2: Filter out the interference signal of the original corner signal through the Butterworth low-pass filter, and obtain the corner data of the high-speed rail bridge; 步骤三：将倾角仪传感器的布置位置和其提取到的转角数据作为输入，通过分段三次样条插值算法计算每两个倾角仪传感器之间的挠度曲线，并绘制高铁桥梁整体的挠度曲线。Step 3: Using the arrangement position of the inclinometer sensors and the extracted rotation angle data as input, calculate the deflection curve between each two inclinometer sensors through the piecewise cubic spline interpolation algorithm, and draw the overall deflection curve of the high-speed rail bridge. 2.根据权利要求1所述的基于倾角仪间接测量高铁桥梁动挠度的方法，其特征在于：步骤三中，假设在高铁桥梁的某一跨上布置有k个倾角仪传感器，以高铁桥梁的一个端点为原点建立局部坐标系，在区间[xi,xi+1]上的挠度曲线为yi(x)，待测点的真实挠度为f1,f2,…,fk，则可以设：2. the method for indirectly measuring the dynamic deflection of a high-speed railway bridge based on an inclinometer according to claim 1, is characterized in that: in step 3, it is assumed that k inclinometer sensors are arranged on a certain span of the high-speed railway bridge, and the high-speed railway bridge is arranged with k inclinometer sensors. One endpoint is the origin to establish a local coordinate system, the deflection curve in the interval [x i , x i+1 ] is y i (x), and the true deflection of the point to be measured is f 1 , f 2 ,..., f k , then Can be set to:
Figure FDA0002718081690000011
Figure FDA0002718081690000011
 记：hi＝xi+1-xi，根据y′i(xi)＝θi,y′i(xi+1)＝θi+1,y″i(xi+1)＝y″i+1(xi+1)，推导得：Note: hi = x i +1 -xi , according to y′ i (x i )=θ i , y′ i (x i +1 )=θ i+1 , y″ i (x i+1 )= y″ i+1 (x i+1 ), deduced:
Figure FDA0002718081690000012
Figure FDA0002718081690000012
Figure FDA0002718081690000013
Figure FDA0002718081690000013
 令：make:
Figure FDA0002718081690000014
Figure FDA0002718081690000014
 则可以得到矩阵方程：Then the matrix equation can be obtained:
Figure FDA0002718081690000021
Figure FDA0002718081690000021
 插值边界条件：f1＝DA,fk＝DB,DA,DB为插值曲线边界的挠度，高铁标准梁为简支梁，边界支座处位移为零，即DA＝DB＝0，由倾角仪转角数据θi通过上述矩阵方程即可得到各个测点的挠度值fi将其带入插值表达式即可得到各段曲线yi(x)，即可得到计算的挠度曲线。Interpolation boundary conditions: f 1 =D A , f k = D B , D A , D B is the deflection of the boundary of the interpolation curve, the standard beam of the high-speed rail is a simply supported beam, and the displacement at the boundary support is zero, that is, D A = D B = 0 , the deflection value f i of each measuring point can be obtained from the angle data θ i of the inclinometer through the above matrix equation, and the curve y i (x) of each segment can be obtained by putting it into the interpolation expression, and the calculated deflection curve can be obtained. 3.根据权利要求1所述的基于倾角仪间接测量高铁桥梁动挠度的方法，其特征在于：步骤一中，布设等距偶数个倾角仪传感器，不等距奇数个倾角仪传感器或不等距偶数个倾角仪传感器。3. the method for indirectly measuring the dynamic deflection of a high-speed railway bridge based on an inclinometer according to claim 1, is characterized in that: in the step 1, lay equidistant even inclinometer sensors, unequal odd odd inclinometer sensors or unequal distances Even number of inclinometer sensors.
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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
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
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CN115218803A (en) * 2022-07-08 2022-10-21 中交第二航务工程局有限公司 Cable-stayed bridge main beam linear monitoring method based on optical fiber sensing

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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
CN115218803A (en) * 2022-07-08 2022-10-21 中交第二航务工程局有限公司 Cable-stayed bridge main beam linear monitoring method based on optical fiber sensing

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Application publication date: 20210115