CN105043631A - Stay cable stay force measuring method based on vibration method using linear model - Google Patents

Abstract

The invention relates to a stay cable stay force measuring method based on a vibration method using a linear model which belongs to the technical field of construction engineering. The method provided in the invention aims to solve problems of prior art. The problems are illustrated as follows. In the prior art, a stay force measuring method, normally based on the assumption of a specific physical model, is difficult to realize a unified recognition of various stay forces and in different measuring methods, the definition of parameters also varies. It is also difficult to operate to mix different measuring methods for use. All these factors undermine measuring accuracy. The method of the invention is carried out as follows. Tensioning a stay cable with two grades of pulling forces; under each grade of pulling force, using a speed accelerator sensor to measure the speed acceleration signals under the action of environment excitation or people excitation; converting the signals into auto power spectrum patterns; substituting each grade frequency of the two grades of pulling forces and the tensioning force into a linear model; identifying linear model coefficients corresponding to each grade frequency and realize the recognition of model parameters. The recognized linear model and the natural vibration frequency of each grade make it possible to recognize the stay cable stay force. With the method provided in the invention, a relatively-high-accuracy measuring value of stay force can be achieved and the problem of recognizing physical parameters to measure stay force using a traditional vibration method can be avoided, thus making the method reduce the uncertainty of a stay force test.

Description

Based on the vibratory drilling method Cable force measuring method of linear model

Technical field

The present invention relates to a kind of vibratory drilling method Cable force measuring method, belong to technical field of structural engineering.

Background technology

Bridge deck and vehicular load are all reached main bearing member by drag-line by cable-stayed bridge, suspension bridge and arched bridge pre-stressed boom, are referred to as Suo Zhicheng bridge.The measurement of Cable force vibration method is the important technical of Suo Zhicheng bridge machinery and construction monitoring.

The cable tension test of vibratory drilling method needs solution two key issues when using: the 1) identification of the drag-line natural frequency of vibration, 2) determination of Suo Li-natural frequency of vibration corresponding relation.Under existing surveying instrument and analysis means condition, the precision measuring frequency can reach 0.005Hz.Therefore, the accuracy of frequency method cable tension test depends primarily on the accuracy of Suo Li and natural frequency of vibration relation, i.e. the precision of model.

The corresponding relation of Suo Li and the natural frequency of vibration by the impact of factors, as the length of drag-line, sag, bendind rigidity and boundary condition etc.Only under two kinds of simplified models, there is explicit corresponding relation in the relation of Suo Li and the natural frequency of vibration:

String model: $T=4{\mathrm{ml}}^2\frac{f_k^2}{k^2}---\left(1\right)$

Hinged girder model: $T=4{\mathrm{ml}}^2\frac{f_k^2}{k^2}-\frac{k^2{\mathrm{\π}}^2}{l^2}EI---\left(2\right)$

In above formula, T represents Suo Li (N), and m represents drag-line line density (kg/m), and l represents guy cable length (m), f _krepresent the k rank natural frequency of vibration (Hz), EI represents rope cross section bendind rigidity (Nm ²), π represents circular constant constant.

In actual work, the relation of Suo Li and frequency is difficult to meet above two kinds of model hypothesis.Wherein, long rope affects by sag, produces nonlinear effect; Tackline is by the impact of boundary condition, cross section bendind rigidity, very larger than actual rope force value deviation based on (1), (2) formula result of calculation.Therefore, the technical difficult points of traditional vibratory drilling method cable force measurement is the identification of parameter, line density m, computational length l ₀, rope cross section bendind rigidity EI, Boundary Stiffness etc.Wherein computational length l ₀represent the Mechanics Calculation length after the removing boundary constraint of drag-line physical length and transition section impact, general and physical length has certain difference.

Existing measuring method is considered factor point situations such as the physical parameter of drag-line and boundary conditions, obtain the corresponding relation of Suo Li under multiple particular case and the natural frequency of vibration, improving one's methods of deriving is revised the coefficient of (2) formula, and overall basic ideas are:

A), set up the dimensionless group reflecting drag-line relative length, divide long rope, middle rope, tackline;

B), some physical parameters are identified, as m, l ₀, EI, boundary condition;

C), based on specific low order vibration frequency (1-3 rank) derivation computing formula.

The subject matter of existing cable force measurement method has:

A), to long rope tackline differentiated treatment, must provide calculating formula according to dimensionless group segmentation, segmentation calculates;

B), specific low order frequency is depended on, as front 3 order frequencies or 1 rank fundamental frequency.In actual cable tension test, limit by site condition, for longer drag-line, acceleration transducer is difficult to be arranged into drag-line mid point, but near bridge floor, the dynamic response recorded like this is based on high order of frequency, and low order frequency precision deficiency will affect Suo Li computational accuracy.The information that simultaneously could not effectively utilize high order of frequency to comprise.

C), real measured data only has a kind of physical quantity of frequency, will identify multiple parameter and Boundary Stiffness accordingly, the many solutions of parameter or accuracy of identification can be caused to decline;

D), each method has specific physical model to suppose, thus the scope of application is limited, and same method is difficult to take into account different model drag-line and different boundary conditions.

In engineering practice, often the cable systems of a bridge block comprises different lengths, diameter specifications, boundary condition, and space sag is different.Which results in the cable tension test method based on specific physics model hypothesis, be difficult to identify multiple Cable power is unified.In addition, the parameter definition of different measuring methods is different, operating difficulties used in combination.

Summary of the invention

The object of this invention is to provide a kind of vibratory drilling method Cable force measuring method based on linear model, be difficult to identify multiple Cable power is unified based on the cable tension test method of specific physics model hypothesis to solve in prior art, the parameter definition of different measuring methods is different, operating difficulties used in combination, affects the problem of measuring accuracy.

The present invention solves the problems of the technologies described above the technical scheme taked to be:

A kind of vibratory drilling method Cable force measuring method based on linear model, the stretching force of in rope construction 2 grades that record drag-line to be measured or more is adjusted at bridge, and test the corresponding to vibration frequency under force level of described drag-line to be measured, thus identify that the coefficient of linear model is to determine linear model; Test the vibration frequency of drag-line to be measured in operation stage, utilize the Suo Li of determined linear model identification drag-line to be measured;

The implementation procedure of described method is:

Step one, according to design data, the scope determining the design Suo Li of drag-line to be measured is [T _min, T _max];

Step 2, in tune rope work progress, at [T _min, T _max] apply different stretching forces in scope under, demarcate the Suo Li T of drag-line to be measured respectively _iwith and corresponding m rank vibration frequency f _i1f _imdata,

Demarcate number of times is for 2 times or more; Subscript i is for distinguishing different stretching forces;

Step 3, Suo Li T according to drag-line to be measured _iwith and corresponding m rank vibration frequency f _i1f _imthe coefficient of data fitting linear model k ∈ [1, m], the expression formula of linear model is

${\hat{T}}_k={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k---\left(1\right)$

represent and pass through f _kthe rope force value estimated,

F _krepresent kth rank vibration frequency; Band subscript i represents measurement data, and no band subscript i does not represent general formula;

Step 4, calculating Suo Li T _iwith linearly dependent coefficient ρ _k;

${\mathrm{\ρ}}_k=\frac{Cov(T_i,\frac{f_{ik}^2}{k^2})}{\sqrt{D\left(T_i\right)}\sqrt{D\left(\frac{f_{ik}^2}{k^2}\right)}}---\left(2\right)$

In formula, Cov () is the covariance function in statistics, by vector T _iwith as stochastic variable, calculate its covariance; D () is the variance function in statistics, calculates T _iwith variance;

Step 5, fitting coefficient

If linearly dependent coefficient ρ _i>0.95 then illustrates T _iwith there is remarkable linear relationship, the linear model that formula (1) is expressed is set up, and takes advantage of matching determination coefficient by least square method

${\hat{B}}_k=\frac{Cov(T_i,\frac{f_{ik}^2}{k^2})}{D\left(T_i\right)}$

${\hat{A}}_k=E\left(T_i\right)-E\left(\frac{f_{ik}^2}{k^2}\right){\hat{B}}_k$

In formula, E () is the expectation function in statistics;

Step 6, test the vibration frequency f of drag-line to be measured in the bridge operation stage ₁f _m;

Step 7, the vibration frequency f that step 4 is obtained ₁f _m, true coefficient substitutes in linear model, obtains m Suo Li estimated value:

${\hat{T}}_k={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k,(k=1...m)$

Step 8, get average available identification Suo Li numerical value:

In step 5,

When demarcation number of times is 2 times (i=1,2), following formula of reduction can be adopted directly to calculate

${\hat{A}}_k=\frac{T_2-T_1}{\frac{f_{2k}^2}{k^2}-\frac{f_{1k}^2}{k^2}}$

${\hat{B}}_k=T_1-{\hat{A}}_k\frac{f_{1k}^2}{k^2}.$

The invention has the beneficial effects as follows:

The inventive method is difference stretch-draw drag-line under 2 grades of tension level, uses acceleration transducer measurement environment to encourage or acceleration signal under artificial excitation's effect, be converted into from power spectrum figure, identify 1 to 5 order frequency in the drawings under every grade of stress level.Each order frequency and pulling force under 2 grades of tension level are substituted into linear model, identifies the linear model coefficients that every order frequency is corresponding, the identification of implementation model parameter.The identification of Cable power can be realized by the linear model after identifying and each rank natural vibration frequency.The present invention is based on linear model approach and can obtain the higher cable force measurement value of precision, avoided the identification problem of traditional vibratory drilling method cable force measurement physical parameter, reduced the model uncertainty in cable tension test.

Instant invention overcomes the deficiencies in the prior art, propose the opportunity utilizing construction cable tension, based on 2 grades of Suo Li and frequency measured data, establish a kind of new cable force measurement method based on linear model.

Actual Suo Zhicheng bridge, in work progress, often needs to adjust stretching rope power, to the multi-level Multi-stage prestress of drag-line.Construction adjusts the jack tension power of rope process to be true Suo Li, tests the inhaul cable vibration frequency under corresponding rope force level, and these data are following Suo Li basis of characterization.

Already proved, for specific drag-line, its kth order frequency square with pulling force linear:

$T={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k$

In formula for linear regression coeffficient.Actual measurement shows, when Dang Suoli changes more stable, this just makes to measure Suo Li based on linear model becomes possibility.The sharpest edges of this method are to have avoided the identification to concrete physical parameter.Possess the condition of stretching rope power in newly building bridge or bridge strengthening etc. under, utilize 2 grades of stretching forces and respective frequencies data thereof to regression coefficient solve, thus bridge operation Cable Force is measured.Compare parameter and the boundary condition identifying of additive method needs, this method is more quick, reliable, and convenient operation, is suitable for field calibration.

Accompanying drawing explanation

Fig. 1 is the vibratory drilling method drag-line cable force measurement operational flowchart based on linear model;

Fig. 2 is inhaul cable vibration auto-power spectrum spectrogram in exemplifying embodiment (stretching rope force level T=180.7kN);

Fig. 3 is linear model and Suo Li drawing for estimate;

Fig. 4 is test unit schematic diagram (1 lifting jack, 2 sensors, 3 test tools, 4 length-measuring appliances, 5 testing tables, 6 test cable wires, 7 test tools);

Fig. 5 is typical drag-line sectional view.

Embodiment

Below in conjunction with accompanying drawing, for the test of the stretching measurement of the drag-line of a root type S4, this method is further elaborated.

The model of pulling test is as Fig. 4, and drag-line two ends load stretching force by numerical control lifting jack.As can be seen, due to the indirect power transmission of connecting screw rod, the boundary condition (hinged, affixed) of drag-line, is difficult to identification directly perceived.

Fig. 5 is typical drag-line cross section, and rope model is S3J, and drag-line cross section comprises 3 × 7+3 root steel wire.This routine drag-line is S4 type, and cross section comprises 4 bundle, 4 × 7 steel wires, and gap and outside are wrapped up by tygon (PE).The long l=11.57m of rope, line density m=5.59kg/m, sectional area A=556mm ², limit Suo Li T _lim=1041.60kN, elastic modulus E=2.0 × 10 ⁵mPa.Cross section bending resistance moment of inertia I is the mechanics parameter of beam, and as seen from Figure 5, the cross section of rope is not that continuous print is overall, there is not the character of bendind rigidity on theory significance.

According to above testing data, the implementation result of this method is verified.

1, according to design data, the design Suo Li scope [T of drag-line to be measured is determined _min, T _max];

The drag-line limit Suo Li of model S4 is T _lim=1041.6kN, design Suo Li gets 10% ~ 30% of ultimate value.Then working cable power scope is roughly [100,300] kN.

2, rope process is adjusted to demarcate many group Cable power T in construction _iwith and corresponding m rank vibration frequency [f _i1f _im] data, make to demarcate rope force value within the scope of design Suo Li [100,300] kN, minimum data is 2 groups;

3, as shown in Figure 2, by inhaul cable vibration auto-power spectrum spectrogram, the multistage natural frequency of vibration of drag-line can be identified.

Test in test 2 groups of rope force value (T ₁, T ₂) and 5 order frequencies of correspondence.

Suo Li T and vibration frequency f demarcated by table 1 _k

Table 1 medium frequency f _kdata transformation is as table 2:

Suo Li T and vibration frequency (f demarcated by table 2 _k/ k) ²

4, according to the coefficient adjusting rope test data linear regression model linear regression expression formula is

${\hat{T}}_k={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k$

Calculate Suo Li T _iwith linearly dependent coefficient ρ _k.

${\mathrm{\ρ}}_k=\frac{Cov(T_i,\frac{f_{ik}^2}{k^2})}{\sqrt{D\left(T_i\right)}\sqrt{D\left(\frac{f_{ik}^2}{k^2}\right)}}$

Substitute into the data of table 2, such as k=1, T _i=[180.70280.10], $\frac{f_{i1}^2}{k^2}=\left[\begin{array}{cc}34.46& 47.89\end{array}\right],$ ?

ρ ₁＝1.0>0.95

Can obtain equally:

ρ ₂＝ρ ₃＝ρ ₄＝ρ ₅＝1.0>0.95

5, design factor

When demarcation number of times is 2 times (i=1,2), following formula of reduction can be adopted directly to calculate

${\hat{A}}_k=\frac{T_2-T_1}{\frac{f_{2k}^2}{k^2}-\frac{f_{1k}^2}{k^2}}$

${\hat{B}}_k=T_1-{\hat{A}}_k\frac{f_{1k}^2}{k^2}$

Substitution table 2 data obtain coefficient as table 3:

Table 3 linear model coefficients

6, in bridge operation stage test inhaul cable vibration frequency f ₁f _m;

In test, in order to simulate the cable tension test in bridge operation stage, adopting double-blind, measuring one group of Suo Li (T ₃, T ₄) and frequency, as table 4.Suo Lizuo is unknown quantity, is measured by this method.

Measuring rope power T and vibration frequency f treated by table 4 _k

Table 4 medium frequency f _kdata transformation is as table 5:

Measuring rope power T and vibration frequency (f treated by table 5 _k/ k) ²

7, vibration frequency is substituted into linear regression model (LRM), obtains m frequency estimation:

${\hat{T}}_k={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k,(k=1...m)$

8, the available Suo Li numerical value of average is got.

$T=\frac{1}{m}\underset{1}{\overset{m}{\Σ}}{\hat{T}}_k$

Table 6 each order frequency Suo Li discre value and average

9, Blind Test contrast

Contrast T ₃, T ₄actual value and measured value, as table 7.

Table 7 Suo Li discre value and actual value contrast

Former formulae discovery contrast

The Suo Li result of calculation of (1) formula of substitution is:

Table 8 Suo Li discre value and actual value contrast

This shows, the Suo Li discre value that classical formulas (1) calculates and actual value deviation are very large, can not be used for actual cable force measurement.

The above; be only the present invention's preferably embodiment; but protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses; be equal to according to technical scheme of the present invention and inventive concept thereof and replace or change, all should be encompassed within protection scope of the present invention.

Claims (2)

1., based on a vibratory drilling method Cable force measuring method for linear model, it is characterized in that:

Adjust the stretching force of in rope construction 2 grades that record drag-line to be measured or more at bridge, and test the corresponding to vibration frequency under force level of described drag-line to be measured, thus identify that the coefficient of linear model is to determine linear model; Test the vibration frequency of drag-line to be measured in operation stage, utilize the Suo Li of determined linear model identification drag-line to be measured;

The implementation procedure of described method is:

Step one, according to design data, the scope determining the design Suo Li of drag-line to be measured is [T _min, T _max];

Step 2, in tune rope work progress, at [T _min, T _max] apply different stretching forces in scope under, demarcate the Suo Li T of drag-line to be measured respectively _iwith and corresponding m rank vibration frequency f _i1f _imdata,

Demarcate number of times is for 2 times or more; Subscript i is for distinguishing different stretching forces;

Step 3, Suo Li T according to drag-line to be measured _iwith and corresponding m rank vibration frequency f _i1f _imthe coefficient of data fitting linear model k ∈ [1, m], the expression formula of linear model is

$\hat{T}={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k---\left(1\right)$

represent and pass through f _kthe rope force value estimated,

F _krepresent kth rank vibration frequency; Band subscript i represents measurement data, and no band subscript i does not represent general formula;

Step 4, calculating Suo Li T _iwith linearly dependent coefficient ρ _k;

${\mathrm{\ρ}}_k=\frac{Cov(T_i,\frac{f_{ik}^2}{k^2})}{\sqrt{D\left(T_i\right)}\sqrt{D\left(\frac{f_{ik}^2}{k^2}\right)}}---\left(2\right)$

In formula, Cov () is the covariance function in statistics, by vector T _iwith as stochastic variable, calculate its covariance; D () is the variance function in statistics, calculates T _iwith variance;

Step 5, fitting coefficient

If linearly dependent coefficient ρ _i>0.95 is T then _iwith there is remarkable linear relationship, the linear model that formula (1) is expressed is set up, and takes advantage of matching determination coefficient by least square method

${\hat{B}}_k=\frac{Cov(T_i,\frac{f_{ik}^2}{k^2})}{D\left(T_i\right)}$

${\hat{A}}_k=E\left(T_i\right)-E\left(\frac{f_{ik}^2}{k^2}\right){\hat{B}}_k$

In formula, E () is the expectation function in statistics;

Step 6, test the vibration frequency f of drag-line to be measured in the bridge operation stage ₁f _m;

Step 7, the vibration frequency f that step 4 is obtained ₁f _m, true coefficient substitutes in linear model, obtains m Suo Li estimated value:

${\hat{T}}_k={\hat{A}}_k{\left(\frac{f_k}{k}\right)}^2+{\hat{B}}_k,(k=1...m)$

Step 8, get average available identification Suo Li numerical value:

2. a kind of vibratory drilling method Cable force measuring method based on linear model according to claim 1, is characterized in that: in step 5,

When demarcation number of times is 2 times, i=1,2, adopt following formula of reduction directly to calculate

${\hat{A}}_k=\frac{T_2-T_i}{\frac{f_{2k}^2}{k^2}-\frac{f_{1k}^2}{k^2}}$

${\hat{B}}_k=T_1-{\hat{A}}_k\frac{f_{1k}^2}{k^2}.$