CN110319808B - Method for predicting and evaluating deformation precision of arch rib of large-span arch bridge measured by tilt sensor - Google Patents
Method for predicting and evaluating deformation precision of arch rib of large-span arch bridge measured by tilt sensor Download PDFInfo
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- CN110319808B CN110319808B CN201910497157.2A CN201910497157A CN110319808B CN 110319808 B CN110319808 B CN 110319808B CN 201910497157 A CN201910497157 A CN 201910497157A CN 110319808 B CN110319808 B CN 110319808B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C9/00—Measuring inclination, e.g. by clinometers, by levels
Abstract
The invention belongs to the technical field of monitoring of deformation of a large-span bridge, and relates to a prediction and evaluation method for measuring deformation precision of an arch rib of a large-span arch bridge by using an inclination angle sensor. When the inclination angle sensor is used for measuring the deformation of the arch rib of the large-span arch bridge, the measurement accuracy of the arch rib under different deformation working conditions is predicted and evaluated, a sensor arrangement scheme capable of meeting the measurement accuracy requirements under various working conditions is comprehensively selected, the structural characteristics of the arch rib are considered, and a base is arranged, so that the sensors arranged on the arch rib are on the same horizontal plane. The method is used for researching the deflection deformation of the arch rib of the large-span arch bridge, considering the influence of sectional errors and inclination angle measurement errors of the inclination angle sensor when the curve is replaced by a straight line in the deformation of the arch rib, designing a sensor arrangement mode capable of meeting the precision requirement of the deflection deformation engineering of the arch rib, predicting the precision range of a measurement result, and evaluating the rationality of the arrangement mode, and the method for the theoretical analysis in advance has important guiding significance for final on-site measurement.
Description
Technical Field
The invention belongs to the technical field of monitoring of deformation of a large-span bridge, and relates to a prediction and evaluation method for measuring deformation precision of an arch rib of a large-span arch bridge by using an inclination angle sensor.
Background
The arch rib is used as a main stress component in the arch bridge structure, the condition of the arch rib determines whether the bridge is safe or not to a great extent, and once a stress structure system is damaged, the whole arch bridge is completely or mostly failed. The deflection deformation of the arch rib is vertical deformation of the arch rib under the action of various load effects, the deformation can visually reflect the vertical rigidity of the arch bridge structure, is one of the most important technical parameters for judging the bearing capacity and integrity of the arch bridge structure, changes and monitors the deflection of the arch rib in real time, and can find whether abnormal conditions occur during the operation of the arch bridge structure.
From the research situation of bridge deformation monitoring technology at home and abroad, the commonly used deformation measurement method for arch ribs of arch bridges mainly comprises the following steps: the method based on the tilt sensor has the advantages of large measuring range, convenience in installation, simplicity in operation and post processing, easiness in implementation, capability of measuring static and dynamic deflection and the like.
With the application scenes of the inclination angle sensor becoming more and more rich, in recent years, a plurality of domestic scholars perform relevant theoretical research on the method for measuring the bridge deformation by the inclination angle sensor, and meanwhile, some scholars perform field measurement tests. Yangxi mountain et al (see detailed literature: Yangxi mountain, Liangliang, Liangpeng, Huang Shaping. A new method for bridge deflection measurement [ J ]. civil engineering, 2002 (02): 92-96.) propose that the inclination and slope of n points can be measured by arranging n inclination sensors on the bridge to be measured; and the flexible line can be obtained by a piecewise curve fitting method or a least square fitting method. The creep climbing (in the literature, the creep climbing, a bridge deflection measurement method based on a beam body corner and experimental research [ D ]. Chongqing traffic university 2010.) provide a method for fitting a deflection curve by a cubic spline curve. Xujin peak (detailed in literature: Xujin Feng. theoretical analysis and research [ D ] Lanzhou university of transportation, 2009.) of the method for measuring bridge deflection by using a novel inclinometer provides a method for measuring bridge deflection by a reasonable cubic spline function method. Invar (for details, see the literature: invar, zhuying peak, populus super. inclinometer applied research [ J ] in bridge health monitoring system modern traffic technology, 2017, 14 (1): 42-44) adopts the inclinometer to calculate midspan deformation through Simpson numerical integration algorithm, and test results show that the error between the inclinometer and the level meter is within 10%, and the measurement precision can meet the engineering requirements. How smart (see the literature for details: design of a bridge linear real-time monitoring system based on a tilt sensor and implementation of [ D ]. Nanjing post and telecommunications university, 2016.) provides a scheme of a bridge linear monitoring system, and designs a high-precision inclinometer and a multi-type interface data acquisition terminal.
The method for measuring the deformation of the arch rib of the large-span arch bridge by using the tilt angle sensor is an indirect measurement method, and the deformation value of the large-span arch bridge is converted into a deflection deformation value after the angle value is measured, so that the converted value has an error with an actual deformation value. The influence of the segmentation error and the angle measurement error of the inclination angle sensor on the measurement result is not considered in the models of the deformation of the beam bridge at present, the precision of the measurement result is not predicted and evaluated, and the problem that whether the finally obtained deformation measurement precision really meets the requirement of actual engineering measurement is ignored. Moreover, most researches take a continuous rigid frame bridge as an experimental object, the continuous rigid frame bridge has small span, large rigidity and small deflection deformation and is less influenced by wind load and temperature load, the arch rib structure of the large-span steel arch bridge has soft rigidity and large deflection deformation and is more influenced by various live loads, and how to research different bridge types is different.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for predicting and evaluating the deformation precision of an arch rib of a large-span arch bridge measured by an inclination angle sensor.
The invention is realized by adopting the following technical scheme:
a method for predicting and evaluating the deformation precision of an arch rib of a large-span arch bridge measured by a tilt sensor comprises the following steps:
s1, establishing an arch bridge space model by using finite element software, carrying out deflection deformation calculation on the arch bridge under different load working conditions to obtain deformation values of the arch rib units under C different load deformation working conditions, and carrying out data storage on the calculation results of the deformation values under the C different load working conditions;
s2, fitting according to the deformation value of the arch rib unit under the a deformation condition to obtain a deflection deformation curve function, and performing derivation processing on the deflection deformation curve function to obtain a corner function of the arch rib under the a deformation condition;
s3, determining a preliminary number of sections according to the form of the deflection deformation curve function, calculating a deflection deformation value of a control point according to the corner function and the number of sections, carrying out error comparison on the deflection deformation value and a theoretical value, if an error result is within a set range, determining the number of sections to be reasonable, and taking the number of sections as the arrangement number of the inclination angle sensors under the deformation working condition a to carry out the next step; otherwise, increasing the number of the segments, and then performing S3;
s4, selecting a tilt angle sensor, and adding the influence of the measurement precision of the sensor on the angle measurement error;
s5, obtaining a theoretical inclination angle value of each inclination angle sensor at the placing position according to the arrangement number and the rotation angle function of the inclination angle sensors, and obtaining an inclination angle measurement value of each inclination angle sensor by adding the influence of the measurement precision of the inclination angle sensors on the angle measurement error, wherein the theoretical distribution of the inclination angle measurement values accords with the positive distribution; selecting a reasonable model, performing multiple times of simulation calculation on the deflection value by using a deflection calculation formula to obtain multiple times of simulation calculation results, and performing mathematical statistics on the simulation calculation results to obtain a mean value, a standard deviation, a confidence interval and a confidence interval error of the simulation calculation results under a deformation condition;
s6, if the error level of the simulation calculation result is within the set error range, the type selection of the tilt angle sensor is reasonable, the arrangement mode is reasonable under the a deformation working condition, and at the moment, the 95% confidence interval and the 95% confidence interval of the relative error of the simulation calculation value are the deflection deformation measurement precision reflection under the method; if the error level of the simulation calculation result does not meet the set error range, improving the accuracy of sensor model selection, and repeating S5;
s7, selecting different arrangement numbers of the inclination sensors to match with the measurement accuracy of the inclination sensors, and obtaining a plurality of arrangement schemes under a deformation condition according to the result under each combination condition;
s8, repeating S1-S7 according to the deformation condition of the arch rib under the b deformation condition, and obtaining a plurality of arrangement schemes under the b deformation condition; by analogy, a measurement precision scheme which meets the requirements of the arch rib under C different deformation working conditions is obtained, and an arrangement scheme with optimal economy is selected as a final arrangement scheme for the arch rib deformation measurement of the arch bridge;
and S9, deploying measuring points at the arch rib of the arch bridge according to the final arrangement scheme, wherein each measuring point comprises a base and an inclination angle sensor.
Further, the base is connected and fixed with the steel arch rib by using bolts, so that the base and the steel arch rib can be cooperatively deformed; the tilt angle sensor is connected and fixed with the base by bolts in a horizontal state.
Further, S2 includes: and (3) importing the calculation result of the arch rib unit in the S1 under the deformation condition a into mathematical analysis software, performing polynomial curve fitting on the scatter deflection value by using a curve fitting toolbox in the mathematical analysis software to obtain a deflection deformation curve function F (x) with the highest fitting degree, and performing derivation processing on the deflection deformation curve function according to material mechanics knowledge to obtain a corner function F (x) of the arch rib under the deformation condition a, wherein F '(x) is F' (x).
Further, S3 includes: obtaining a dip angle value theta of a measuring point of the dip angle sensor under the a deformation working condition through a corner functioni(ii) a Determining the number N of sections of the curve according to the form of the deflection deformation curve function F (x), namely the arrangement number of the inclination angle sensors, and preliminarily selecting the number of sections equal to the times of the deformation curve function F (x); according to the rotation angle function f (x) and the number of segments N, where the length of each segment is LiCalculating the deflection deformation value y of the control point, wherein the calculation formula is that y is equal to sigma Li tanθiComparing the deflection deformation value y with the theoretical value, if the error result is in the set range under the deformation working condition of a, the number of the segments is considered to be reasonable,carrying out the next step; otherwise, the number of segments N is increased, and S3 is performed.
Further, the theoretical value in S3 is obtained from the deflection curve function.
Further, the influence of the measurement accuracy of the sensor on the angle measurement error is obtained by performing Monte Carlo sampling on the measurement accuracy of the tilt sensor.
Preferably, the measurement accuracy of the tilt sensor comprises the composition of nonlinear, repetitive, hysteresis, zero offset and cross-axis error factors, and the calculation formula is as follows:
let θ beiIs the true value of the angle of inclination, θmiIs a measurement of the angle of inclination, then thetamiIs a random variable belonging to a normal distribution, the expected value of the distribution is the true value theta of the inclination angleiThe standard deviation is the square of the measurement accuracy of the tilt sensor, i.e. thetami～N(θi,2)，θmiThe probability density function of (a) is:
preferably, reasonable models in S5 include the Monte Carlo method and Latin hypercube sampling.
Preferably, the deflection calculation formula in S5 is:
y＝∑Li tanθmi
wherein L isiFor each segment length, θmiIs a tilt angle measurement.
Preferably, the inclination angle measurement value is obtained by averaging a plurality of measurements in S5.
Compared with the prior art, the deflection deformation measuring technology of the tilt sensor has the beneficial effects that:
1) the method is used for researching the deflection deformation of the arch rib of the large-span arch bridge, considering the influence of sectional errors and inclination angle measurement errors of the inclination angle sensor when the curve is replaced by a straight line in the deformation of the arch rib, designing a sensor arrangement mode capable of meeting the precision requirement of the deflection deformation engineering of the arch rib, wherein the sensor arrangement mode comprises the selection and the arrangement quantity of sensors, analyzing the error of the final deflection deformation measurement result of the arch rib by integrating the influence of the two factors, predicting the precision range of the measurement result and evaluating the rationality of the arrangement mode, and the method of the prior theoretical analysis has important guiding significance for final on-site measurement.
2) And in each deformation condition of the arch rib, a sensor arrangement scheme meeting the measurement precision is provided. And setting various main deformation working conditions aiming at the deformation of the arch rib of the arch bridge, and finally selecting a sensor arrangement scheme capable of meeting the measurement precision requirement under the various deformation working conditions.
3) Due to errors generated during angle measurement, the measurement precision is improved by adopting a method of averaging in multiple measurements. The influence of the reading dispersity of the measuring instrument on the measuring result can be reduced by taking the average value through multiple measurements, and the measuring reliability is improved. Averaging of multiple measurements can result in a reduced fluctuation range of error compared to a single measurement.
4) The deformation curve of the arch rib is calculated and analyzed by using finite element software, the segmentation number of the arch rib is selected according to the deformation curve, the required segmentation number (namely the number of the sensors) can be quickly obtained from the deformation curve shape and the function formula, and the efficiency of selecting the number of the sensors is improved.
5) The influence of the sectional error caused by the sectional fitting when the arch rib deformation replaces the curve by the straight line and the angle measurement error caused by the measurement of the inclination angle sensor on the final deflection deformation result is considered, so that the accuracy of the result is improved when the deflection deformation is measured.
6) And (3) performing reasonable random simulation measurement on the deflection deformation result by using a Monte Carlo method as a deflection deformation measurement result evaluation method. And (3) obtaining relevant data characteristics such as the mean value, the standard deviation, the confidence interval error and the like of the result through simulating the measurement result, evaluating the final deflection deformation result according to the arrangement modes of different sensor numbers and different sensor precisions, and predicting the measurement precision range of the final deflection deformation result.
7) Aiming at the characteristic that the horizontal included angle at the arch springing position of the arch bridge is large, the base is arranged, so that the sensors arranged on the arch ribs are all kept at the horizontal plane position, and the problem that the inclination angle sensor at the arch springing position cannot obtain the inclination angle value due to the fact that the inclination angle sensor exceeds the range is solved.
Drawings
FIG. 1 is a flow chart of a method for predicting and evaluating the deformation accuracy of an arch rib of an arch bridge according to an embodiment of the present invention;
FIG. 2 is a view of a base mounting according to an embodiment of the present invention;
FIG. 3 is a view of a tilt sensor installation in accordance with an embodiment of the present invention;
FIG. 4 is an elevation of a bridge in meters in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of a bridge model according to an embodiment of the present invention;
FIG. 6 is a deformation diagram of a rib under one embodiment of the present invention;
FIG. 7 is a graph of a condition-rib deformation fit (in m) according to an embodiment of the present invention;
fig. 8 is a graph of single deflection measurements (N12, 0.005) in an embodiment of the invention;
fig. 9 is a graph of single deflection measurements (N12, 0.001) in an embodiment of the invention;
fig. 10 is a graph of single deflection measurements (N12, 0.0001) in an embodiment of the present invention;
fig. 11 is a graph of single deflection measurements (N20, 0.005) in an embodiment of the invention;
fig. 12 is a graph of single deflection measurements (N20, 0.001) in an embodiment of the invention;
fig. 13 is a graph of single deflection measurements (N20, 0.0001) in an embodiment of the present invention;
fig. 14 is a graph of single deflection measurements (N28, 0.005) in an embodiment of the invention;
fig. 15 is a graph of single deflection measurements (N28, 0.001) for an embodiment of the present invention;
fig. 16 is a graph of single deflection measurements (N28, 0.0001) in an embodiment of the present invention;
fig. 17 is a graph of multiple deflection measurements (N12, 0.005) in accordance with an embodiment of the present invention;
fig. 18 is a graph of multiple deflection measurements (N12, 0.001) in an embodiment of the present invention;
fig. 19 is a graph of multiple deflection measurements (N12, 0.0001) in accordance with an embodiment of the present invention;
fig. 20 is a graph of multiple deflection measurements (N20, 0.005) in an embodiment of the invention;
fig. 21 is a graph of multiple deflection measurements (N20, 0.001) in accordance with an embodiment of the present invention;
fig. 22 is a graph of multiple deflection measurements (N20, 0.0001) in accordance with an embodiment of the present invention;
fig. 23 is a graph of multiple deflection measurements (N28, 0.005) in accordance with an embodiment of the present invention;
fig. 24 is a graph of multiple deflection measurements (N28, 0.001) in accordance with an embodiment of the present invention;
fig. 25 is a graph of multiple deflection measurements (N28, 0.0001) in accordance with an embodiment of the present invention;
FIG. 26 is a main arch sensor layout (half span) in one embodiment of the invention.
Detailed Description
The present invention will be described in further detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.
And measuring the deflection change values of certain specific points to obtain a deflection deformation curve of the arch rib under the action of load. The idea of measuring the deflection deformation of the arch rib is as follows: the deflection measured values at the key cross section (maximum deflection deformation, half and third) are ensured to meet the measurement requirement, and the measured values of other deflection measuring points can be within reasonable measurement errors, so that the monitoring and measuring efficiency is improved.
The invention uses the inclination angle sensor to measure the angle, and then uses the segment superposition method to measure the arch rib deformation, so the measurement error of the arch rib deflection deformation comprises the segment error and the angle measurement error. If the accuracy of the arch rib deformation measurement is to be analyzed, the influence of segmentation and angle measurement needs to be fully considered, and in order to better select a proper measurement arrangement scheme, an analog measurement mode needs to be adopted to predict and analyze the accuracy range of the arch rib deflection measurement, and the specific analysis is as follows:
(1) and obtaining a deformation curve of the arch rib under the action of load, and describing the obtained deformation curve by using a polynomial function so as to obtain an inclination angle function of the deformation curve. Selecting different segmentation numbers, carrying out segmentation error analysis on the arch rib deformation curve, obtaining the deflection value of each measuring point by using a superposition method, and calculating the error caused by segmentation by comparing the deflection value with the deflection value at the key section.
(2) On the basis of the sectional errors, the errors of the angle measurement of the inclination angle sensors are considered, the inclination angle sensors with different measurement accuracies are selected, the angle measurement is randomly taken, the deflection is measured in an analog mode, the Monte Carlo method is used for evaluating the deflection measurement errors when different sectional numbers and different sensor accuracies are adopted, and relevant mathematical statistics is carried out on the measurement results.
(3) The dip angle measurement is divided into two different measurement modes of single measurement and multiple measurement averaging, and the influence of the multiple measurement averaging mode on the accuracy of the final deflection measurement result is analyzed.
(4) And comprehensively selecting a scheme meeting the requirement of the arch rib deformation measurement precision.
(5) Aiming at the characteristic that the horizontal included angle at the arch springing position of the arch bridge is large, a base is arranged, so that sensors arranged on arch ribs are kept at the horizontal plane position.
A method for predicting and evaluating deformation accuracy of a large-span arch bridge arch rib measured by an inclination sensor comprises the following steps of predicting and evaluating the measurement accuracy of the arch rib under different deformation working conditions when the inclination sensor is used for measuring the deformation of the large-span arch bridge arch rib, comprehensively selecting a sensor arrangement scheme capable of meeting the measurement accuracy under various working conditions, and arranging measurement points based on a base for measuring the deformation of the large-span arch bridge arch rib, as shown in figure 1, wherein the method comprises the following steps:
and S1, establishing a mechanical analysis model of the arch bridge. The finite element calculation software commonly used is Midas civil or ANSYS. And calculating the deflection of the bridge under different load working conditions by using finite element software, calculating the deformation of the bridge unit to obtain the deformation values of the arch rib unit under C different load working conditions, and storing the calculation results of the deformation values under C different load working conditions in data.
S2, importing the calculation results of the arch rib units in the S1 under the a deformation condition into mathematical analysis software, for example: matlab, using a curve fitting tool box in mathematical analysis software to perform polynomial curve fitting on a scatter deflection value to obtain a deflection deformation curve function F (x) with the highest fitting degree, and performing derivation processing on the deflection deformation curve function according to material mechanics knowledge to obtain a corner function F (x) of an arch rib under a deformation condition of a (F' (x)).
S3, obtaining the inclination angle value theta of the measuring point of the sensor under the a deformation condition through the rotation angle functioni. Determining the number N of the sections of the curve according to the form of the deflection deformation curve function F (x), namely the number of the sensors, and preliminarily selecting the number of the sections which is equal to the times of the deformation curve function F (x). According to the rotation angle function f (x) and the number of segments N (each segment is of length L in this case)i) Calculating the deflection deformation value y of the control point, wherein the calculation formula is that y is equal to sigma Li tanθiAnd comparing the error of the calculated deflection value with a theoretical value, wherein the theoretical value is obtained by a deflection curve function. According to the calculation result, if the error result is within the set range (the general error range is +/-5%) under the deformation working condition a, the number of the sections is considered to be reasonable, and the next step can be carried out; otherwise, the number of segments N is increased, and S3 is performed.
S4, selecting a proper tilt angle sensor according to the sensor arrangement number N selected under the a deformation condition in the S3, carrying out Monte Carlo sampling according to the measurement accuracy of the tilt angle sensors of different brands and models, and determining the angle measurement error. According to the definition of the measurement accuracy of the tilt sensor, the accuracy of the tilt sensor is the synthesis of factors such as nonlinearity, repeatability, hysteresis, zero offset, cross axis error and the like, and the calculation formula is as follows:
let θ beiIs the true value of the angle of inclination, θmiIs a tilt angle measurement. ThetamiIs a random variable belonging to a normal distribution, the expected value of the distribution is the true value theta of the inclination angleiThe standard deviation being the square of the measurement accuracy of the sensor, i.e. thetami～N(θi,2) Then thetamiThe probability density function of (a) is:
s5, determining the number N of the selected sensors in S4, and determining a theoretical inclination angle value theta of each sensor at the placing position according to a rotation angle function f (x) of the sensorsi. The influence of the measurement precision of the sensors on the angle measurement error is added, so that the measured value theta of the inclination angle at each sensor can be obtainedmiTheoretical distribution of it
The distribution fits into a positive distribution. Selecting reasonable model (such as Monte Carlo method and Latin hypercube sampling), and converting y ═ Sigma L by using deflectioni tanθmiAnd performing simulation calculation on the deflection value for multiple times, generally selecting random simulation calculation for ten thousand times to obtain a simulation calculation result y for multiple times, and performing mathematical statistics on the simulation calculation result y to obtain a mean value, a standard deviation, a confidence interval and a confidence interval error of the simulation calculation result y under the a deformation condition.
S6, if the obtained result meets the set error range (the relative error is generally less than or equal to +/-5%), the type selection of the sensor is reasonable, and the arrangement mode is reasonable under the a deformation working condition. At the moment, the 95% confidence interval and the 95% confidence interval of the simulated calculation value y are the deflection deformation measurement accuracy reflection under the method. If the result does not satisfy the set error range, the accuracy of sensor model selection needs to be improved, and S5 is repeated.
S7, different sensor numbers N and measurement accuracies of multiple sensors can be selected for matching, and multiple arrangement schemes under a deformation condition a are obtained according to results under each combination condition.
And S8, repeating S1-S7 according to the deformation condition of the arch rib under the b deformation condition, and obtaining various arrangement schemes under the b deformation condition. By analogy, a measurement precision scheme that the arch rib meets requirements under C different deformation working conditions is obtained, and an arrangement scheme with optimal economy is selected as a final arrangement scheme for arch rib deformation measurement of the arch bridge.
And S9, deploying measuring points at the arch rib of the arch bridge according to the final arrangement scheme, wherein each measuring point comprises a base and an inclination angle sensor.
The measuring range of the tilt angle sensor is +/-10 degrees, and due to the structural characteristics of the arch rib, the horizontal included angle at the arch top is small, and the horizontal included angle at the arch foot is large. If the tilt sensor is directly mounted on the surface of the arch rib, the tilt sensor at the arch foot cannot obtain the tilt value due to the out-of-range, and therefore, a base member is required to be arranged so that the sensors mounted on the arch rib are all maintained in a horizontal position. In this embodiment, each measuring point includes a base and a tilt sensor, and as shown in fig. 2 and 3, the base is connected and fixed with the steel arch rib by using bolts, so as to ensure that the base and the steel arch rib can cooperatively deform. The tilt angle sensor is connected and fixed with the base by bolts in a horizontal state.
Taking the rib deformation measurement of a certain large-span arch bridge as an example, the large bridge is a 177m +428m +177m three-span arch bridge, and the elevation view of the large bridge is shown in fig. 4.
The bridge space finite element model is established by using general finite element software MIDAS/CIVIL as shown in FIG. 5. The MIDAS/CIVIL is intuitive and powerful structural design and analysis software, is developed aiming at special bridge structural forms such as a prestressed box bridge, a suspension bridge, a cable-stayed bridge and the like, is also suitable for various underground building structures, and is commercial finite element analysis software which is commonly used in the analysis design of the bridge structure at present.
The method is used for analyzing the arch rib of the arch bridge under three different deformation conditions and analyzing the arrangement scheme of the reasonably selected sensors on the arch rib of the bridge. The three working conditions are respectively as follows: the most unfavorable working condition of live load at one half of the main arch, the most unfavorable working condition of live load at one third of the main arch and the overall heating working condition of the main arch. The most unfavorable working condition of live load at one half of the main arch is analyzed as follows:
1) fitting of deformation curves
And (3) solving an influence line of the deformation of the main arch rib span, and applying a road-I-level lane load at the position where the influence line is positive to form a condition that the live load is the most unfavorable at one half of the main arch, wherein the deformation of the main arch rib under the condition is shown in figure 6.
And fitting a deflection curve of the whole bridge from the deflection values of the segment sectional points obtained from the finite element software so as to conveniently obtain a corner curve and further obtain a corner value. Taking the starting point of one side of the main arch as the origin of the longitudinal direction, taking the longitudinal direction distance between the node and the starting point of the main arch as an x coordinate, taking the deflection deformation value as a y coordinate, fitting a deformation curve graph by using Matlab, and obtaining a deformation curve function by using a curve fitting tool, wherein a curve image is shown in FIG. 7.
When the deflection curve function is fitted, a mid-span point is selected as a segmentation point, and a polynomial function is used for segmentation fitting of the curve. The fitted curve and the node deflection coordinate have an R-square equal to 1 by adjusting the Degree value of the polynomial function. Due to the discontinuity of data, the fitted model has deviation from the actual value, and in the embodiment, the degree of approximation of the regression equation to the fitting of the observed value is described by using the goodness of fit R-square. The closer the R-square is to 1, the higher the approximation of the fit.
The polynomial function at this time is:
in the formula:
p1＝-7.894×10-13；p2＝7.034×10-10；p3＝-1.626×10-7；
p4＝1.026×10-5；p5＝-6.234×10-5；p6＝8.706×10-5；
p7＝7.881×10-13；p8＝-7.025×10-10；p9＝-1.622×10-7；
p10＝1.530×10-5；p11＝-9.031×10-3；p12＝0.7343。
the dip function is:
2) segmentation error analysis
The single-side fitting flexible line function is a 5-degree polynomial function, theoretically, when the number of single-side sections is considered to be 5 sections, the relative error between the calculated value and the actual value of the control point in the span of the main arch rib can be generally controlled within a proper range, but because the main arch span is large, a large number of sections should be selected under the support of sufficient conditions, and therefore the number of the whole sections N is considered to be 12, 20 and 28 to analyze the error respectively. And (4) performing sectional error calculation analysis by taking the mid-span point of the arch rib of the main arch as a deflection control point. The results of the computational analysis are shown in table 1:
TABLE 1 operating conditions with a segmentation error
From table 1 it can be derived: if the error of angle measurement is not considered, and only the segmentation error is considered, the error of the control point in the span of the main arch rib is gradually reduced along with the increase of the number of segments. Therefore, the number of curve segments is increased, and the calculation accuracy of the control point across the arch rib can be improved. When the number of main arch sections N is 12, the error of the calculated deflection and the theoretical deflection in the arch rib span can be controlled within a smaller range.
3) Angle error analysis
Three types of inclination angle sensors commonly used in the market at present are selected, and the measurement accuracy is 0.005 degrees, 0.001 degrees and 0.0001 degrees respectively. And (3) carrying out deflection simulation measurement on the sensors with different measurement accuracies by using a Monte Carlo method, and analyzing the measurement errors.
Single deflection measurement analysis
The single deflection measurement is carried out by using sensors with different precisions for the number of sections, namely the number of sensor arrangement, N is 12, 20 and 28. The single deflection measurement refers to collecting the inclination angle values of all measuring points of the arch rib at the same time under the working condition, and obtaining the deflection value through conversion. Under random simulation measurement, a fitting curve graph of single deflection measurement for 5 times is compared with a theoretical deflection curve, and the result is shown in fig. 8-16.
Taking the Monte Carlo coefficient M as 10000, carrying out 10000 times of random value taking on each measuring point, and carrying out 10000 times of analog measurement on the deflection. Mathematical statistics are performed on the mid-span measurement control points, and the results are shown in tables 2 to 3.
TABLE 2 Single deflection simulation measurement average distribution of over-center measuring points (unit: m)
TABLE 3 Single deflection simulation measurements 95% probability confidence interval relative error (unit:%)
From fig. 8 to 16 and tables 2 to 3, it can be seen that: when the number of the sections is the same and the sensors with different precisions are selected, the deflection curve in the single deflection measurement result can accord with the change trend of the theoretical deflection, but the discreteness of the deflection measurement result has a certain difference, the sensor with higher precision is selected, and the curve of the analog measurement is closer to the theoretical curve; the relative error of 95% probability confidence interval of the cross-center measuring point is continuously reduced along with the improvement of precision. When the inclination angle sensor with the precision of 0.005 degrees is selected, the discreteness of deflection results of each measuring point is obvious, and the error between the deflection results of each measuring point and a theoretical value is large; when the inclination angle sensor with the precision of 0.0001 degree is selected, the discreteness of deflection results of each measuring point is very small and basically consistent with a theoretical value; when a high-precision sensor is selected, the error generated by measuring of a single section is small, and the deflection result obtained by the accumulated measurement of the latter section is slightly influenced by the former section. When the sensors with the same precision are selected and the number of the segments is different, the increase of the number of the segments reduces the relative error of the 95% probability confidence interval; the number of segments increases, i.e. the number of sensors arranged increases, the closer the measurement result is to the theoretical value.
The influence of the accuracy of the sensor on the deflection measurement result is more than the specific number N of the sections. When a sensor with the angle of 0.005 degrees is adopted, the single-time measurement deflection of the sensor has the probability of 95 percent within the error range of +/-23 percent, and the error range can not meet the measurement requirement of practical engineering application; and the inclination angle sensor with the measurement precision of 0.0001 degree is adopted, the probability of 95 percent of single-time measurement deflection error is controlled within the range of +/-1 percent of relative error, and the discreteness of the simulation measurement result can be controlled within a small range. If the inclination angle sensor with the measurement precision of 0.001 degrees is adopted and the number of the sections is 12, the deflection error of the inclination angle sensor can be controlled within the range of +/-5% with the probability of 95%, and the inclination angle sensor can better meet the application of actual engineering. Therefore, considering the single measurement method, the tilt sensor with the accuracy of 0.001 ° can be selected so as to satisfy the measurement requirement with the number of segments N of 12.
(II) multiple measurement error analysis
Due to the error generated during angle measurement, in this embodiment, the measurement accuracy is further improved by adopting a method of averaging multiple measurements. The influence of the reading dispersity of the measuring instrument on the measuring result can be reduced by taking the average value through multiple measurements, and the measuring reliability is improved. As can be seen from statistical knowledge, the fluctuation range of the error of the single measurement value is larger than that of the average value, and the error of the single measurement value is larger than that of the average value. Averaging of multiple measurements reduces the fluctuation range of the error compared to a single measurement.
And averaging the inclination angle values measured for multiple times to analyze the deflection result. The single measurement 1 refers to a deflection deformation result obtained by taking a single-time measurement inclination angle value, the multiple measurement 5 refers to a deflection deformation result obtained by taking five single-time measurement inclination angle values as an average value, and the like. Now, the single measurement 1, the multiple measurements 5 and the multiple measurements 20 are taken respectively for error analysis. The deflection curve of the deflection curve measured by a certain random simulation measurement is compared with the theoretical deflection curve, and the results are shown in fig. 17-25. Mathematical statistics analysis was performed on the averaged mid-span measurement control points, and the results are shown in tables 4 to 7.
Table 4 mean value of distribution of multiple deflection simulation measurements across the midpoint (mean number n is 5) (unit: m)
Table 5 multiple deflection simulation measurements 95% probability confidence interval relative error (average number n ═ 5) (unit:%)
TABLE 6 mean value of distribution of multiple deflection simulation measurements across the midpoint (average number of n is 20) (unit: m)
Table 7 multiple deflection simulation measurements 95% probability confidence interval relative error (average number n ═ 20) (unit:%)
From fig. 17 to 25 and tables 4 to 7, it can be seen that: the method of averaging multiple measurements reduces the fluctuation range of the error compared to a single measurement. It can be seen from the graph that as the average times increase, the deflection measurement curve is closer to the theoretical value curve, the deflection result dispersion of multiple measurements is smaller than that of single measurement, and the sensor has lower precision and more obvious effect.
When the sensors and the number of sections with the same precision are selected, and only the average times are considered, the relative error of the 95% probability confidence interval across the middle measuring point is smaller along with the increase of the average times, and the measured value is closer to the theoretical value. Although the error can be reduced by the method of averaging multiple measurements, the effect is not obviously improved when a high-precision sensor is adopted, and when the sensor with the measurement precision of 0.0001 degree is adopted, the error range of single measurement and multiple measurements is within +/-1 percent; when a sensor with lower precision is adopted, the error can be effectively reduced by increasing the times, and when the sensor with the measurement precision of 0.005 degrees is adopted, the error of single measurement can be reduced from the range of +/-23 percent to the range of +/-6 percent of 20 times of measurement.
If the inclination angle sensor with the measurement precision of 0.005 degrees is adopted, the number of the sections is 20, and the average number of times of measurement is 20, the deflection error of the inclination angle sensor has the probability of 95 percent and the relative error is within the range of +/-5 percent, and the effect of the inclination angle sensor is basically consistent with the single measurement effect of the inclination angle sensor with the measurement precision of 0.001 degrees.
In principle, the more the average times, the smaller the fluctuation range of the error, the smaller the deflection error of the measurement, but the measurement times are related to the acquisition time, if the sensor is synchronously acquired by adopting a sampling frequency of 1Hz, the time required by 20 measured values is 20 seconds, and the time required by 60 measured values is 1 minute, and the actual structure may generate a large deflection deformation influence on the measurement result in the time, so the acquisition time should be reduced as much as possible, and the structure is in the same deformation state during the measurement.
Therefore, under the working condition, 12 inclination angle sensors with the measurement accuracy of 0.001 degree can be arranged, and a scheme of a multi-time measurement method can be adopted.
Similarly, aiming at the most unfavorable working condition of live load at one third of the main arch and the overall heating working condition of the main arch, the measurement precision analysis and the arrangement scheme determination which are the same as the working condition I are respectively carried out on the two working conditions. And finally, selecting an arrangement scheme with optimal economy as a final arrangement scheme for the arch bridge arch rib deformation measurement according to the measurement accuracy meeting the three working conditions. The final solution is shown in fig. 26, divided into 28 segments of the main arch, arranging tilt sensors with an accuracy of 0.001 °.
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 (8)
1. A method for measuring deflection deformation precision of arch ribs of a large-span arch bridge by using a tilt sensor is characterized in that the deflection deformation measuring idea of the arch ribs is as follows: the deflection measured value at the key section is ensured to meet the measurement requirement, and the measured values of other deflection measuring points are also in reasonable measurement error; the method comprises the following steps:
s1, establishing an arch bridge space model by using finite element software, carrying out deflection deformation calculation on the arch bridge under the live load most unfavorable working condition of one half of a main arch, the live load most unfavorable working condition of one third of the main arch and the overall heating working condition of the main arch to obtain deformation values of an arch rib under three different load deformation working conditions, and carrying out data storage on the calculation results of the deformation values under the three different load working conditions;
s2, fitting according to the arch rib deformation value under the most unfavorable working condition of live load at one half of the main arch to obtain a deflection deformation curve function, and carrying out derivation processing on the deflection deformation curve function to obtain a corner function of the arch rib under the most unfavorable working condition of live load at one half of the main arch;
s3, determining a preliminary number of sections according to the form of a deflection deformation curve function, calculating a deflection deformation value of a control point according to a corner function and the number of sections, and carrying out error comparison on the deflection deformation value and a theoretical value, wherein the theoretical value is obtained by the deflection deformation curve function, if an error result is in a set range, the number of sections is reasonable, and the number of sections is used as the arrangement number of inclination angle sensors under the most adverse working condition of live load at one half of a main arch for the next step; otherwise, increasing the number of the segments, and then performing S3;
s4, selecting a tilt angle sensor, and adding the influence of the measurement precision of the tilt angle sensor on the angle measurement error;
s5, obtaining a theoretical inclination angle value of each inclination angle sensor at the placing position according to the arrangement number and the rotation angle function of the inclination angle sensors, and obtaining an inclination angle measurement value of each inclination angle sensor by adding the influence of the measurement precision of the inclination angle sensors on the angle measurement error, wherein the theoretical distribution of the inclination angle measurement values accords with the positive distribution; performing simulation calculation on the deflection value for multiple times by using a deflection calculation formula by adopting a Latin hypercube sampling and a Monte Carlo method to obtain multiple simulation calculation results, and performing mathematical statistics on the simulation calculation results to obtain a mean value, a standard deviation, a confidence interval and a confidence interval error of the simulation calculation results under the most unfavorable working condition of live load at one half of a main arch;
s6, if the error level of the simulation calculation result is within the set error range, the type selection of the tilt angle sensor is reasonable, the arrangement mode is reasonable under the most unfavorable working condition of live load at one half of the main arch, and at the moment, the 95% confidence interval and the 95% confidence interval of the relative error of the simulation calculation result are the deflection deformation measurement precision reflection; if the error level of the simulation calculation result does not meet the set error range, improving the accuracy of sensor model selection, and repeating S5;
s7, selecting different arrangement numbers of the inclination sensors to match with the measurement accuracy of the inclination sensors, and obtaining a plurality of arrangement schemes under the condition that live load is the most unfavorable at one half of the main arch according to the result under each combination condition;
s8, repeating S1-S7 according to the deformation condition of the arch rib under the most unfavorable working condition of live load at one third of the main arch, and obtaining a plurality of arrangement schemes under the most unfavorable working condition of live load at one third of the main arch; by analogy, obtaining a measurement precision scheme meeting requirements under three different deformation conditions of a live load most unfavorable working condition of the arch rib at one half of the main arch, a live load most unfavorable working condition of the main arch at one third of the main arch and a main arch overall heating working condition, and selecting an arrangement scheme with optimal economy as a final arrangement scheme for arch rib deformation measurement of the arch bridge;
s9, deploying measuring points at arch ribs of the arch bridge according to the final arrangement scheme, wherein each measuring point comprises a base and an inclination angle sensor; the base brings the tilt sensors mounted on the ribs in the same horizontal plane.
2. The arch bridge arch rib deflection deformation precision measurement method of claim 1, wherein the base of the measuring point is connected and fixed with the arch rib by using bolts, so that the base and the arch rib can be deformed cooperatively; the tilt angle sensor is connected and fixed with the base by bolts in a horizontal state.
3. An arch bridge rib deflection deformation accuracy measuring method according to claim 1, wherein S2 includes: and (3) importing the calculation result of the arch rib in the S1 under the condition of the most unfavorable live load at the half position of the main arch into mathematical analysis software, performing polynomial curve fitting on the deflection value of the scattered point by using a curve fitting tool box in the mathematical analysis software to obtain a deflection deformation curve function F (x) with the highest fitting degree, and performing derivation processing on the deflection deformation curve function according to the material mechanics knowledge to obtain a corner function F (x) of the arch rib under the condition of the most unfavorable live load at the half position of the main arch, wherein F (x) is F' (x).
4. An arch bridge rib deflection deformation accuracy measuring method according to claim 1, wherein S3 includes: the inclination angle value theta of the measuring point of the inclination angle sensor under the most unfavorable working condition of live load at one half of the main arch is obtained through the corner functioni(ii) a Determining the number N of sections of the curve according to the form of the deflection deformation curve function F (x), taking the number N of sections as the arrangement number of the tilt angle sensors, and preliminarily selecting the number of sections equal to the times of the deformation curve function F (x); according to the rotation angle function f (x) and the number of segments N, where the length of each segment is LiCalculating the deflection deformation value y of the control point, wherein the calculation formula is that y is equal to sigma LitanθiComparing the deflection deformation value y with a theoretical value, and if the error result is in a set range under the most adverse working condition of live load at one half of the main arch, considering that the number of the sections is reasonable, and carrying out the next step; otherwise, the number of segments N is increased, and S3 is performed.
5. The arch bridge arch rib deflection deformation accuracy measurement method of claim 1, wherein the influence of the measurement accuracy of the tilt sensor on the angle measurement error in S4 is obtained by monte carlo sampling the measurement accuracy of the tilt sensor.
6. The arch bridge arch rib deflection deformation accuracy measurement method of claim 5, wherein the measurement accuracy of the tilt sensor comprises non-linear error1Repeatability error2Hysteresis error3Zero offset error4And cross axis error5The composition of the factors is as follows:
let θ beiIs the true value of the angle of inclination, θmiIs a measurement of the angle of inclination, then thetamiIs a random variable belonging to a normal distribution, the expected value of the distribution is the true value theta of the inclination angleiThe standard deviation is the square of the measurement accuracy of the tilt sensor, i.e. thetami～N(θi,2)，θmiThe probability density function of (a) is:
7. the arch bridge arch rib deflection deformation accuracy measurement method of claim 1, wherein the deflection calculation formula in S5 is as follows:
y＝∑Litanθmi
wherein L isiFor each segment length, θmiIs a tilt angle measurement.
8. The arch bridge rib deflection deformation accuracy measurement method of claim 1, wherein in S5, the inclination angle measurement value is obtained by averaging a plurality of measurements.
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