CN103335858A - Method for measuring bridge structure dynamic displacement and vibration frequency - Google Patents

Abstract

A method for measuring bridge structure dynamic displacement and vibration frequency is provided. The method includes the following steps of: (1) establishing a bridge structure vibration field monitoring system so as to synchronously acquire vibration displacement and global navigation satellite system (GNSS) time; (2) performing coordinate system projection conversion which comprises the steps of calculating projection parameters between a local coordinate system and a bridge independent coordinate system and transforming measured structure vibration coordinate projection into the bridge independent coordinate system; (3) filtering bridge structure vibration displacement gross errors; (4) re-sampling vibration displacement through using a linear interpolation method; (5) separating quasi-static parts from dynamic parts in displacement by using a Chebyshev filter; and (6) analyzing vibration signal frequency spectrums through using a fast Fourier method. The method of the invention has the advantages of non-contact property, high precision, high reliability, high automation and the like.

Description

The measuring method of a kind of bridge structure dynamic displacement and vibration frequency

Technical field

The present invention is mainly concerned with the bridge structural health monitoring technical field, refers in particular to a kind of measuring method at bridge structure dynamic displacement and vibration frequency.

Background technology

The bridge structure dynamic property is monitored and diagnosed, also in time carries out lesion assessment and safe early warning, to improving the bridge efficiency of operation, avoid great casualties and property loss that significance is arranged.Wherein, quasistatic displacement, dynamic displacement, vibration frequency are the important parameters of reaction bridge structure dynamic property.And the displacement of long period quasistatic and short period dynamic displacement in the vibration of monitoring bridge structure are the difficult points of present bridge structural health monitoring.

Conventional bridge structure dynamic parameter measurement instrument mainly is accelerometer, but there is following defective in it:

(1) accelerometer can only be measured the bridge structure vibration signal by the way of contact is arranged, and for the position that bridge tower etc. is difficult to arrive, operates very inconveniently, and it is bigger to measure difficulty.

(2) utilize accelerometer directly to measure the acceleration of structural vibration, only can obtain the relative displacement of structural vibration behind the integration, can't obtain absolute displacement, cause accelerometer to be difficult to carry out long continuous monitoring.

(3) in the process of monitoring, need to adopt Hi-pass filter to eliminate the trend term that produces in twice integral process, accelerometer can only be measured the short period dynamic displacement in the structural vibration, can't measure the displacement of long period quasistatic.

In the prior art, other has a kind of automatic type total powerstation, this automatic type total powerstation has automatic target identification, Automatic Target Following, measurement automatically, automatic record, measuring accuracy advantages of higher, its measuring accuracy reaches the millimeter level, even submillimeter level precision, so it often is used to the high-precision deformation monitoring of engineering structures such as side slope, dam, bridge, tunnel, but can not be used for bridge structure dynamic deformation and vibration frequency measurement, main cause is:

Reasons such as (1), measurement data omission low owing to temporal resolution, noise adopt present measuring method, and the automatic type total powerstation can only be measured the quasistatic displacement of engineering structure, can't measure short period dynamic displacement and the vibration frequency of engineering structure.

(2) because the electric signal that the automatic type total powerstation adopts the quartz crystal oscillating circuit to produce comes timing, its time precision is difficult to reach the structural vibration Testing requirement.

Summary of the invention

The technical problem to be solved in the present invention just is: at the technical matters that prior art exists, the invention provides a kind of contactless, high precision, high reliability, the bridge structure dynamic displacement of high automation and the measuring method of vibration frequency.

For solving the problems of the technologies described above, the present invention by the following technical solutions:

The measuring method of a kind of bridge structure dynamic displacement and vibration frequency the steps include:

(1) sets up bridge structure vibration field monitoring system, gather vibration displacement and GNSS time synchronously; Utilize the tracing mode of automatic total powerstation to gather bridge structure vibration displacement information, the time of utilizing the GNSS signal receiver to gather the high-precision GNSS time synchronously and upgrade the automatic type total powerstation;

(2) coordinate system projection conversion; At first calculate the projective parameter between local coordinate system and the bridge coordinate system, then institute's geodesic structure vibrational coordinate projection is transformed into the bridge coordinate system;

(3) filter bridge structure vibration displacement rough error; Prior imformation according to the bridge structure vibration arranges the displacement boundary value, excluding gross error; According to the temporal information in the each row of data record, filter the identical data line of temporal information that causes owing to the data recording mistake;

(4) linear interpolation method is to the vibration displacement resampling; According to the nominal sampling rate of automatic type total powerstation, adopt the method for linear interpolation that institute's measurement information is carried out resampling, repair missing value;

(5) the employing Chebyshev filter separates quasistatic part and the dynamic part in the displacement;

(6) adopt fast Fourier methods analyst vibration signal frequency spectrum; Respectively x (n), y (n), z (n) the displacement sequence measured are carried out spectrum analysis, obtain vertical, horizontal, the vertical vibration frequency of bridge structure.

As a further improvement on the present invention:

Described step (2) be with the monitoring point in local coordinate system coordinate and the time (E, N, H, T) be transformed into coordinate in the bridge coordinate system and time (x, y, z, t), adopt following formula (1) to carry out the coordinate projection conversion:

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\\ t_i\end{array}\right]=\left[\begin{array}{cccc}\cos \mathrm{\α}& \sin \mathrm{\α}& 0& 0\\ -\sin \mathrm{\α}& \cos \mathrm{\α}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{E}_i\\ N_i\\ H_i\\ T_i\end{array}\right]---\left(1\right)$

I=1 in the formula, 2,3 ..., N, N is the record total amount, α represents the position angle of monitored bridge 8 y directions in local coordinate system:

α＝arctan[(E ₂-E ₁)/(N ₂-N ₁)] (2)

α represents the position angle of monitored bridge y direction in local coordinate system, (E in the formula ₁, N ₁), (E ₂, N ₂) be 2 coordinates in local coordinate system on the bridge floor y direction; Local coordinate is monitored bridge location rectangular coordinate system commonly used; The bridge coordinate system is to be the x direction with the bridge longitudinal axis, is the y direction with the bridge transverse axis, is the rectangular coordinate system of z direction with the bridge vertical pivot.

Carry out described step (1) before, making the temporal resolution of automatic type total powerstation bring up to 0.01s by 1s earlier, and demarcating the automatic type total powerstation at the standard baseline, obtaining its range finding addition constant.

The idiographic flow of described step (1) is: in first datum round prism is set, as backsight point; 360 ° of prisms are installed in monitoring point at the bridge floor that is positioned at the monitored bridge on the river and/or bridge tower, settle an automatic type total powerstation in second datum, and at GNSS signal receiver of the top of automatic type total powerstation installation, known D coordinates value according to first reference point, second reference point, utilize the first benchmark null circle prism orientation, build a station at the monitoring scene, form the four-dimensional vibration monitor system that comprises three-dimensional vibrating displacement and GNSS temporal information.

The idiographic flow of described step (4) is: adopt approach based on linear interpolation to repair missing value, t ₁The moment and t ₂Omit t shift value constantly constantly, the shift value in the calculating t moment (x, y, z):

$\left\{\begin{array}{c}x=x_1+\frac{(t-t_1)x_2-(t-t_1)x_1}{t_2-t_1}\\ y=y_1+\frac{(t-t_1)y_2-(t-t_1)y_1}{t_2-t_1}\\ z=z_1+\frac{(t-t_1)z_2-(t-t_1)z_1}{t_2-t_1}\end{array}\right.---\left(3\right)$

(x in the formula ₁, y ₁, z ₁) be t ₁Shift value constantly, (x ₂, y ₂, z ₂) be t ₂Moment shift value, adopting the nominal sampling rate is the automatic type total powerstation of 10Hz, data recording is spaced apart 0.1s, so value t of the above-mentioned moment ₁, t ₂, t is the multiple of 0.1s.

The idiographic flow of described step (5) is: choose 0.01Hz for separating the cutoff frequency of quasistatic displacement and dynamic displacement, I type Chebyshev Hi-pass filter is:

$G_n\left(w\right)=\left|H_n\left(\mathrm{jw}\right)\right|=\frac{1}{\sqrt{1+{\mathrm{\ϵ}}^2{T}_n^2\left(\frac{w}{w_0}\right)}}---\left(4\right)$

ε is that ripple coefficient, n are exponent number, ω in the following formula ₀Be cutoff frequency, T _n(w/w ₀) expression n rank Chebyshev polynomials:

$T_n\left(\frac{w}{w_0}\right)=\left\{\begin{array}{cc}\cos (n\&CenterDot;\arccos \frac{w}{w_0})& (0\&le;w<w_0)\\ \cosh (n\&CenterDot;\arccos \frac{w}{w_0})& (w_0\&le;w)\end{array}\right.---\left(5\right)$

Design ripple coefficient ε is 0.1, cutoff frequency ω ₀For 0.01Hz, exponent number n are 8, quasistatic part and dynamic part in the I type Chebyshev Hi-pass filter decomposition vibration displacement of passband ripple.

Compared with prior art, the invention has the advantages that:

1, the simultaneously displacement of long period quasistatic, short period dynamic displacement and the vibration frequency of monitoring of structures dynamic response of the present invention, and then successfully solved the difficult point that dynamic displacement and quasistatic displacement are difficult to monitor simultaneously.

2, measuring accuracy height of the present invention can reach the displacement measurement precision of mm level, precision all routine measurement methods in the prior art.

3, the present invention can measure the three-dimensional absolute displacement of structural vibration, and obtains vertical, horizontal, the vertical dynamic response of bridge simultaneously, obtains the distortion absolute value, finally can realize the long term monitoring of bridge structure distortion.

4, the GNSS time that in the monitor signal of measuring method of the present invention, has comprised the nanosecond precision, and then be that this monitor signal has been created condition with monitor signal comparison and the fusion of miscellaneous equipment.Namely, measuring method of the present invention is gathered process implementation structure dynamic displacement and vibration frequency measurements such as high-precision GNSS time, coordinate system projection conversion, Chebyshev filter decomposition displacement, linear interpolation repairing missing value, Fast Fourier Transform (FFT) spectrum analysis by external GNSS signal receiver, measure the displacement of long period quasistatic, short period dynamic displacement and the vibration frequency of structural vibration simultaneously.

5, by adopting measuring method of the present invention, can provide a new contactless dynamic response monitoring means for bridge structural health monitoring, and then realized the measurement of bridge structure dynamic parameter noncontact, high precision, high reliability, high automation, to become a kind of new contactless structure dynamic property monitoring means, have broad application prospects.

Description of drawings

Fig. 1 is the schematic flow sheet of measuring method of the present invention.

Fig. 2 is the instrument layout synoptic diagram of the present invention in concrete application example.

Fig. 3 is the present invention's bridge structure vibration displacement synoptic diagram in concrete application example.

Fig. 4 is the present invention's bridge structure vibration quasistatic displacement diagram in concrete application example.

Fig. 5 is the present invention's bridge structure vibration dynamic displacement synoptic diagram in concrete application example.

Fig. 6 is the present invention's bridge structure vibration displacement spectrum diagram in concrete application example.

Marginal data:

1, justifies prism; 2, first reference point; 3, GNSS signal receiver; 4, automatic type total powerstation; 5, second reference point; 6,360 ° of prisms; 7, bridge floor monitoring point; 8, monitored bridge; 9, river.

Embodiment

Below with reference to Figure of description and specific embodiment the present invention is described in further details.

As shown in Figure 1, the measuring method of bridge structure dynamic displacement of the present invention and vibration frequency may further comprise the steps:

(1) plug-in of automatic type total powerstation 4 is upgraded and demarcate, automatic type total powerstation 4 is used for gathering displacement data.

Plug-in to automatic type total powerstation 4 is optimized, and makes its time resolution bring up to 0.01s by 1s, the core frame form of upgrading plug-in.

Demarcate automatic type total powerstation 4 at the standard baseline, obtain its range finding addition constant.Wherein, the computing formula of addition constant is: k=D _AC-D _AB-D _BC, D _AC, D _AB, D _BCBe respectively line segment AC, the AB that automatic type total powerstation 4 measures, the horizontal range of BC, and A, B, C are on same straight line at 3; That is, line segment AB, BC are on same straight line, and two line AB and BC form line segment AC.Adopt automatic type total powerstation 4 to measure the horizontal range D of line segment AC, AB, BC respectively _AC, D _AB, D _BC, the addition constant that calculates automatic type total powerstation 4 is: k=D _AC-D _AB-D _BC

(2) set up bridge structure vibration field monitoring system, gather vibration displacement and GNSS time synchronously.

Referring to Fig. 2,2 places arrange round prism 1 at first reference point, as backsight point; 360 ° of prisms 6 are installed in bridge floor monitoring point 7 at the bridge floor that is positioned at the monitored bridge 8 on the river 9 and/or bridge tower, 360 ° of prisms 6 are connected with pedestal, pedestal is fixed on the monitored bridge 8 by U-shaped support, regulates the foundation leg spiral, makes the vertical pivot vertical of 360 ° of prisms 6.Settle an automatic type total powerstation 4 at second reference point, 5 places, and at GNSS signal receiver 3 of the top of automatic type total powerstation 4 installation, GNSS signal receiver 3 can with automatic type total powerstation 4 by carrying the interface seamless link, known D coordinates value according to first reference point 2, second reference point 5, utilize the first benchmark null circle prism, 1 orientation, build a station at the monitoring scene, form the four-dimensional vibration monitor system that comprises three-dimensional vibrating displacement and GNSS temporal information.GNSS signal receiver 3 is gathered the GNSS time of nanosecond precision in real time, and the time of real-time update automatic type total powerstation 4, and automatic type total powerstation 4 is gathered bridge structure vibration three-D displacement and time signal synchronously.

After adopting said structure, utilize the tracing mode of automatic type total powerstation 4 to gather bridge structure vibration displacement information, utilize GNSS signal receiver 3 to gather the high-precision GNSS time synchronously, structural vibration displacement and GNSS time carry interface by instrument and realize seamless fusion like this, and the time of real-time update automatic type total powerstation 4.

Automatic type total powerstation 4 is gathered bridge structure GNSS time and vibration displacement synchronously, and each data is constantly pressed following format record:

Numbering P _i, the GNSS time T _i, eastern coordinate E _i, northern coordinate N _i, elevation H _iWherein, i=1,2,3 ..., N, N is the record total amount.

(3) coordinate system projection conversion.

It is the structural vibration displacement signal of benchmark that automatic type total powerstation 4 is gathered with local coordinate, at first calculate the projective parameter between local coordinate system and the bridge coordinate system, then institute's geodesic structure vibrational coordinate projection is transformed into the bridge coordinate system, with bridge floor monitoring point 7 in local coordinate system coordinate and the time (E, N, H, T) be transformed in the bridge coordinate system coordinate and the time (x, y, z, t), adopt following formula (1) to carry out the coordinate projection conversion:

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\\ t_i\end{array}\right]=\left[\begin{array}{cccc}\cos \mathrm{\&alpha;}& \sin \mathrm{\&alpha;}& 0& 0\\ -\sin \mathrm{\&alpha;}& \cos \mathrm{\&alpha;}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{E}_i\\ N_i\\ H_i\\ T_i\end{array}\right]---\left(1\right)$

I=1 in the formula, 2,3 ..., N, N is the record total amount, α represents the position angle of monitored bridge 8 y directions in local coordinate system:

α＝arctan[(E ₂-E ₁)/(N ₂-N ₁)] (2)

α represents the position angle of monitored bridge 8 y directions in local coordinate system, (E in the formula ₁, N ₁), (E ₂, N ₂) be 2 coordinates in local coordinate system on the bridge floor y direction.Local coordinate is monitored bridge 8 locations rectangular coordinate systems commonly used; The bridge coordinate system is to be the x direction with the bridge longitudinal axis, is the y direction with the bridge transverse axis, is the rectangular coordinate system of z direction with the bridge vertical pivot.

(4) filter bridge structure vibration displacement rough error.

Prior imformation according to the bridge structure vibration arranges the displacement boundary value, excluding gross error; According to the temporal information in the each row of data record, filter the identical data line of temporal information that causes owing to the data recording mistake.

The prior imformation of bridge structure vibration adopts Finite Element Method to calculate displacement peak value τ according to bridge structure physical size and material, and getting 3 τ is the displacement boundary value, directly rejects the shift value greater than 3 τ.The tracing mode employing rate of automatic type total powerstation 4 reaches 10Hz, the instrument real time record comprises the data of period P, time t, along slope coordinate x, lateral coordinates y, vertical coordinate z, because Data Update and recording frequency height, can duplicate the phenomenon with missing data, time t according in the data recording directly rejects the repeating data record.

(5) linear interpolation method is to the vibration displacement resampling.

Because Data Update and recording frequency height, the phenomenon that data are omitted can appear, because the data skewness of omitting, carry out dynamic displacement and spectrum analysis if directly adopt these data, precision and accuracy all obviously reduce, must adopt the method for linear interpolation that institute's measurement information is carried out resampling according to the nominal sampling rate of automatic type total powerstation 4, repair missing value.

Adopt approach based on linear interpolation to repair missing value, t ₁The moment and t ₂Omit t shift value constantly constantly, the shift value in the calculating t moment (x, y, z):

$\left\{\begin{array}{c}x=x_1+\frac{(t-t_1)x_2-(t-t_1)x_1}{t_2-t_1}\\ y={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003310701000012.png"\; state="\{\{state\}\}">y</figure-callout>}}_1+\frac{(t-t_1)y_2-(t-t_1)y_1}{t_2-t_1}\\ z={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00003310701000012.png"\; state="\{\{state\}\}">z</figure-callout>}}_1+\frac{(t-t_1)z_2-(t-t_1)z_1}{t_2-t_1}\end{array}\right.---\left(3\right)$

(x in the formula ₁, y ₁, z ₁) be t ₁Shift value constantly, (x ₂, y ₂, z ₂) be t ₂Moment shift value, adopting the nominal sampling rate is the automatic type total powerstation of 10Hz, data recording is spaced apart 0.1s, so value t of the above-mentioned moment ₁, t ₂, t is the multiple of 0.1s.Displacement after the resampling as shown in Figure 3, transverse axis is represented the time (time) among the figure, the longitudinal axis is represented displacement (Displacement), comprises structural vibration length travel (x-axis), transversal displacement (y-axis), vertical displacement (z-axis) totally three partial datas.

(6) the employing Chebyshev filter separates quasistatic part and the dynamic part in the displacement.

Reach several minutes or longer by the period of change of the long period quasistatic displacement that causes under the external loads effect, it changes change frequency less than 0.01Hz, the engineering structure vibration frequency is generally 0.1Hz～10Hz, so choose 0.01Hz for separating the cutoff frequency of quasistatic displacement and dynamic displacement, I type Chebyshev Hi-pass filter is:

$G_n\left(w\right)=\left|H_n\left(\mathrm{jw}\right)\right|=\frac{1}{\sqrt{1+{\mathrm{\&epsiv;}}^2{T}_n^2\left(\frac{w}{w_0}\right)}}---\left(4\right)$

ε is that ripple coefficient, n are exponent number, ω in the following formula ₀Be cutoff frequency, T _n(w/w ₀) expression n rank Chebyshev polynomials:

$T_n\left(\frac{w}{w_0}\right)=\left\{\begin{array}{cc}\cos (n\&CenterDot;\arccos \frac{w}{w_0})& (0\&le;w<w_0)\\ \cosh (n\&CenterDot;\arccos \frac{w}{w_0})& ({\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="HDA00003310701000022.png"\; state="\{\{state\}\}">w</figure-callout>}}_0\&le;w)\end{array}\right.---\left(5\right)$

Design ripple coefficient ε is 0.1, cutoff frequency ω ₀For 0.01Hz, exponent number n are 8, quasistatic part and dynamic part in the I type Chebyshev Hi-pass filter decomposition vibration displacement of passband ripple.Adopt the Chebyshev filter of above-mentioned design to separate the decomposition texture vibration displacement as shown in Figure 3, the quasistatic displacement that decomposites as shown in Figure 4, the dynamic displacement that decomposites is as shown in Figure 5.

(7) fast Fourier methods analyst vibration signal frequency spectrum.

Adopt specific window function to carry out time domain to the conversion of frequency domain to revising the back structure vibration signals, carry out the structure vibration signals spectrum analysis, obtain the structural vibration frequency.Respectively x (n), y (n), z (n) the displacement sequence measured are carried out spectrum analysis, can obtain vertical, horizontal, the vertical vibration frequency of bridge structure, as shown in Figure 6, be bridge structure vibration displacement spectrum diagram.

All directions analytical approach unanimity is example with z (n) displacement sequence below.Z (n) to time domain carries out discrete fourier variation acquisition frequency-domain function Z (k):

$Z\left(k\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}z\left(n\right)e^{-j\frac{2\mathrm{\&pi;}}{N}\text{kn}}$ k＝0，1，2…，N-1

The length of z in the formula (n) is M, and N is discrete fourier constant interval length, value N=M, and order:

$W_N=e^{-j\frac{2\mathrm{\&pi;}}{N}}$

Then

$Z\left(k\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}z\left(n\right)W_N^{\mathrm{kn}}$ k＝0，1，2…，N-1

Adopt the time domain abstracting method that leaf transformation in the N point discrete Fourier is decomposed into short Fourier and change, reduce operand, following formula is decomposed two data sequences of z (n) by the parity of n calculate, reduce operand, raise the efficiency.

Below only be preferred implementation of the present invention, protection scope of the present invention also not only is confined to above-described embodiment, and all technical schemes that belongs under the thinking of the present invention all belong to protection scope of the present invention.Should be pointed out that for those skilled in the art the some improvements and modifications not breaking away under the principle of the invention prerequisite should be considered as protection scope of the present invention.

Claims (6)

1. the measuring method of a bridge structure dynamic displacement and vibration frequency is characterized in that step is:

(1) sets up bridge structure vibration field monitoring system, gather vibration displacement and GNSS time synchronously; Utilize the tracing mode of automatic total powerstation to gather bridge structure vibration displacement information, the time of utilizing the GNSS signal receiver to gather the high-precision GNSS time synchronously and upgrade the automatic type total powerstation;

(2) coordinate system projection conversion; At first calculate the projective parameter between local coordinate system and the bridge coordinate system, then institute's geodesic structure vibrational coordinate projection is transformed into the bridge coordinate system;

(3) filter bridge structure vibration displacement rough error; Prior imformation according to the bridge structure vibration arranges the displacement boundary value, excluding gross error; According to the temporal information in the each row of data record, filter the identical data line of temporal information that causes owing to the data recording mistake;

(4) linear interpolation method is to the vibration displacement resampling; According to the nominal sampling rate of automatic type total powerstation, adopt the method for linear interpolation that institute's measurement information is carried out resampling, repair missing value;

(5) the employing Chebyshev filter separates quasistatic part and the dynamic part in the displacement;

(6) adopt fast Fourier methods analyst vibration signal frequency spectrum; Respectively x (n), y (n), z (n) the displacement sequence measured are carried out spectrum analysis, obtain vertical, horizontal, the vertical vibration frequency of bridge structure.

2. the measuring method of bridge structure dynamic displacement according to claim 1 and vibration frequency, it is characterized in that, described step (2) is with coordinate and the time (E of monitoring point in local coordinate system, N, H T) is transformed into coordinate and time (x in the bridge coordinate system, y, z, t), adopt following formula (1) to carry out the coordinate projection conversion:

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\\ t_i\end{array}\right]=\left[\begin{array}{cccc}\cos \mathrm{\&alpha;}& \sin \mathrm{\&alpha;}& 0& 0\\ -\sin \mathrm{\&alpha;}& \cos \mathrm{\&alpha;}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{E}_i\\ N_i\\ H_i\\ T_i\end{array}\right]---\left(1\right)$

I=1 in the formula, 2,3 ..., N, N is the record total amount, α represents the position angle of monitored bridge 8 y directions in local coordinate system:

α＝arctan[(E ₂-E ₁)/(N ₂-N ₁)] (2)

α represents the position angle of monitored bridge y direction in local coordinate system, (E in the formula ₁, N ₁), (E ₂, N ₂) be 2 coordinates in local coordinate system on the bridge floor y direction; Local coordinate is monitored bridge location rectangular coordinate system commonly used; The bridge coordinate system is to be the x direction with the bridge longitudinal axis, is the y direction with the bridge transverse axis, is the rectangular coordinate system of z direction with the bridge vertical pivot.

3. the measuring method of bridge structure dynamic displacement according to claim 1 and vibration frequency, it is characterized in that, carrying out described step (1) before, make the temporal resolution of automatic type total powerstation bring up to 0.01s by 1s earlier, and at standard baseline demarcation automatic type total powerstation, obtain its range finding addition constant.

4. the measuring method of bridge structure dynamic displacement according to claim 1 and vibration frequency is characterized in that, the idiographic flow of described step (1) is: in first datum round prism is set, as backsight point; 360 ° of prisms are installed in monitoring point at the bridge floor that is positioned at the monitored bridge on the river and/or bridge tower, settle an automatic type total powerstation in second datum, and at GNSS signal receiver of the top of automatic type total powerstation installation, known D coordinates value according to first reference point, second reference point, utilize the first benchmark null circle prism orientation, build a station at the monitoring scene, form the four-dimensional vibration monitor system that comprises three-dimensional vibrating displacement and GNSS temporal information.

5. the measuring method of bridge structure dynamic displacement according to claim 1 and vibration frequency is characterized in that, the idiographic flow of described step (4) is: adopt approach based on linear interpolation to repair missing value, t ₁The moment and t ₂Omit t shift value constantly constantly, the shift value in the calculating t moment (x, y, z):

$\left\{\begin{array}{c}x=x_1+\frac{(t-t_1)x_2-(t-t_1)x_1}{t_2-t_1}\\ y=y_1+\frac{(t-t_1)y_2-(t-t_1)y_1}{t_2-t_1}\\ z=z_1+\frac{(t-t_1)z_2-(t-t_1)z_1}{t_2-t_1}\end{array}\right.---\left(3\right)$

(x in the formula ₁, y ₁, z ₁) be t ₁Shift value constantly, (x ₂, y ₂, z ₂) be t ₂Moment shift value, adopting the nominal sampling rate is the automatic type total powerstation of 10Hz, data recording is spaced apart 0.1s, so value t of the above-mentioned moment ₁, t ₂, t is the multiple of 0.1s.

6. the measuring method of bridge structure dynamic displacement according to claim 1 and vibration frequency, it is characterized in that, the idiographic flow of described step (5) is: choose 0.01Hz for separating the cutoff frequency of quasistatic displacement and dynamic displacement, I type Chebyshev Hi-pass filter is:

$G_n\left(w\right)=\left|H_n\left(\mathrm{jw}\right)\right|=\frac{1}{\sqrt{1+{\mathrm{\&epsiv;}}^2{T}_n^2\left(\frac{w}{w_0}\right)}}---\left(4\right)$

ε is that ripple coefficient, n are exponent number, ω in the following formula ₀Be cutoff frequency, T _n(w/w ₀) expression n rank Chebyshev polynomials:

$T_n\left(\frac{w}{w_0}\right)=\left\{\begin{array}{cc}\cos (n\&CenterDot;\arccos \frac{w}{w_0})& (0\&le;w<w_0)\\ \cosh (n\&CenterDot;\arccos \frac{w}{w_0})& (w_0\&le;w)\end{array}\right.---\left(5\right)$

Design ripple coefficient ε is 0.1, cutoff frequency ω ₀For 0.01Hz, exponent number n are 8, quasistatic part and dynamic part in the I type Chebyshev Hi-pass filter decomposition vibration displacement of passband ripple.

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