CN103900785A - Method for determining transverse dynamic displacement of girder of large-span bridge structure - Google Patents

Abstract

The invention discloses a method for determining transverse dynamic displacement of a girder of a large-span bridge structure. The method includes the following steps that (1), GPS displacement monitoring data in a girder span are collected; (2) vector decomposition and mean value processing are conducted on the monitoring data to obtain transverse dynamic displacement data; (3) fitting is conducted on the power spectral density of the transverse dynamic displacement data by the adoption of the Gaussian series; (4) the harmony superposition method is used for obtaining the dynamic displacement fitted value of the girder. According to the method, a mathematical modeling method is used on the basis of the monitoring data, and transverse dynamic displacement of the girder can be determined more accurately.

Description

A kind of definite long-span bridges girder is the method for moving displacement laterally

Technical field

The invention belongs to the load effect analysis field of long-span bridges member, relate to a kind of method of definite long-span bridges member load effect, specifically, relate to a kind of laterally method of moving displacement of definite long-span bridges girder.

Background technology

The long-span bridges system of cable load-bearing is widely adopted in Bridge Design type, because its soft characteristic main beam member is being subject to there will be obvious transversal displacement response while carrying compared with strong wind, thereby badly influence normal use and the security performance of long-span bridges during runing.Therefore study long-span bridges laterally moving displacement size of girder span centre under wind load response, have important practical significance.The girder span centre that various countries researchist has responded wind load aspect theory derivation, finite element analogy and wind tunnel test at present laterally moving displacement has carried out to a certain degree research.But, because wind carries excitation, girder transversal displacement being affected to machine-processed complicacy, traditional theory derivation, finite element analogy and wind tunnel test is difficult to truly reflect that long-span bridges is subject to the laterally moving displacement size of wind action under actual operation state.

In recent years along with Loads of Long-span Bridges health monitoring technical development, monitoring instrument can be installed on structural elements and directly obtain environmental load and the load response Monitoring Data of long-span bridges under true environment, thereby effectively avoid traditional theory derivation, finite element analogy and wind tunnel test to exist initial parameter assignment deviation, initial boundary condition to set the incorrect problem of ignoring of deviation and minor effect factor.But at present for main beam member, laterally monitoring and the analytical work of moving this part of displacement is very few, laterally the Changing Pattern of moving displacement under true environment condition is still unknown for main beam member, not yet has the laterally method of moving displacement of the girder of a kind of definite long-span bridges under true environment condition of researching and proposing.

Summary of the invention

Technical matters: the present invention proposes a kind ofly can accurately reflect the laterally Changing Pattern of moving displacement of main beam member, can utilize Monitoring Data to obtain the laterally method of moving displacement of definite long-span bridges girder of the result under true environment condition.

Technical scheme: a kind of definite long-span bridges main beam member of the present invention is the method for moving displacement laterally, comprises the steps:

Step (1): the Monitoring Data that gathers girder span centre GPS displacement:

GPS displacement monitoring station is installed at the girder span centre place of Loads of Long-span Bridges, motion vector u (t) is herein carried out to Real-Time Monitoring and with time series storage, u (t)=[u _x(t), u _y(t), u _z(t)], u _x(t), u _y(t), u _z(t) be respectively three direction of principal axis displacements under gps coordinate system, t represents the time, t=1, and 2 ..., L, unit is second, L represents time span;

Step (2): Monitoring Data is carried out to resolution of vectors and average value processing, laterally moved displacement time-histories u _d(t);

Step (3): utilize the laterally power spectrum density of moving displacement data of Gauss's progression matching:

(a) first utilize and improve the laterally moving displacement time-histories u of period map method calculating _d(t) power spectrum density P (f), wherein f represents frequency values, P represents spectral density value, then draws power spectral density plot taking f, P as horizontal, ordinate respectively;

(b) utilize the Peak Intensity Method of power spectrum density from described power spectral density plot, determine non-remarkable frequency band district and be designated as f ₁, described non-remarkable frequency band district f ₁power spectrum density corresponding in power spectral density plot is designated as P ₁, described f ₁with P ₁one-to-one relationship in power spectral density plot adopts P ₁(f ₁) represent;

(c) utilize the Peak Intensity Method of power spectrum density from power spectral density plot, determine remarkable frequency band district and be designated as f ₂, remarkable frequency band district f ₂power spectrum density corresponding in power spectral density plot is designated as P ₂, f ₂with P ₂one-to-one relationship in power spectral density plot adopts P ₂(f ₂) represent;

(d) to non-remarkable frequency band district f ₁and corresponding power spectrum density P ₁carry out 4 rank Gaus series expressions matchings, determine non-remarkable frequency band district f ₁power spectrum density fitting function

idiographic flow is:

D1) by f ₁with P ₁get respectively denary logarithm, and 4 rank Gaus series expressions shown in substitution following formula:

$1g\left(P_1\right)=\underset{p=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\λ}}_p{e}^{-{\left(\frac{1g\left(f_1\right)-{\mathrm{\α}}_p}{{\mathrm{\β}}_p}\right)}^2}$

In formula, λ _p, α _pand β _pfor Gaussian parameter, p is the discrete variable of 4 rank Gauss's progression, p=1,2,3,4, lg (f ₁) and lg (P ₁) represent respectively f ₁with P ₁denary logarithm;

D2) the Gaussian parameter λ to 4 rank Gaus series expressions _p, α _pand β _pcarry out least square fitting, draw respectively and λ _p, α _pand β _pcorresponding best Gaussian parameter value

with

D3) utilize following formula to obtain non-remarkable frequency band district f ₁power spectrum density fitting function

${\hat{P}}_1\left(f_1\right)=10^{\left(\underset{p=1}{\overset{4}{\mathrm{\Σ}}}{\widehat{\mathrm{\λ}}}_p{e}^{-{\left(\frac{1g\left(f_1\right)-{\widehat{\mathrm{\α}}}_p}{{\widehat{\mathrm{\β}}}_p}\right)}^2}\right)}$

(e) to remarkable frequency band district f ₂and corresponding power spectrum density P ₂carry out the Gaus series expressions matching of (3+s) rank, determine remarkable frequency band district f ₂power spectrum density fitting function

wherein s is remarkable frequency band district f ₂the total number of spectral density peak value, idiographic flow is:

E1) by f ₂with P ₂get respectively denary logarithm, and (3+s) rank Gaus series expressions shown in substitution following formula:

$1g\left(P_2\right)=\underset{m=1}{\overset{3+s}{\mathrm{\Σ}}}{a}_m{e}^{-{\left(\frac{1g\left(f_2\right)-b_m}{c_m}\right)}^2}$

In formula, a _m, b _mand c _mfor Gaussian parameter, m is the discrete variable of (3+s) rank Gauss's progression, m=1, and 2 ..., 3+s, lg (f ₂) and lg (P ₂) represent respectively f ₂with P ₂denary logarithm;

E2) the Gaussian parameter a to (3+s) rank Gaus series expressions _m, b _mand c _mcarry out least square fitting, draw respectively and a _m, b _mand c _mcorresponding best Gaussian parameter value

with

E3) utilize following formula to obtain remarkable frequency band district f ₂power spectrum density fitting function

${\hat{P}}_2\left(f_2\right)=10^{\left(\underset{m=1}{\overset{3+s}{\mathrm{\Σ}}}{a}_m{e}^{-{\left(\frac{1g(f_2-b_m)}{c_m}\right)}^2}\right)}$

(f) obtain utilizing the laterally power spectrum density of moving displacement data of Gauss's progression matching

be shown below:

Step (4): utilize harmonic wave method of superposition to obtain laterally moving displacement match value of girder:

By frequency f at frequency separation [f _minf _max] on be evenly divided into q part, obtain every part of frequency band length l and be:

$l=\frac{f_{\max }-f_{\min }}{q}$

In formula, f _maxfor the maximal value of frequency f, f _minfor the minimum value of frequency f, q is total umber of frequency band length;

Utilize following formula to calculate every part of centre frequency that frequency band length l is corresponding

${\tilde{f}}_j=l\·(j-0.5)$

In formula, j is the sequence number of every part of frequency band length, j=1, and 2 ..., q,

represent centre frequency corresponding to j part frequency band length l;

Utilize the harmonic wave superpositing function shown in following formula to obtain the laterally moving displacement match value of girder in any t moment

${\tilde{u}}_d\left(t\right)=\underset{j=1}{\overset{q}{\mathrm{\Σ}}}\sqrt{2\hat{P}\left({\tilde{f}}_j\right)\·l}\sin (2\mathrm{\π}{\tilde{f}}_{j}t+{\mathrm{\θ}}_j)$

In formula, θ _jfor obey j random sampling value of even stochastic distribution on [0,2 π] interval,

for in centre frequency

under the laterally power spectrum density of moving displacement data of Gauss's progression matching.

In the preferred version of the inventive method, the time span L in step (1) is at least 1 day, and is the integral multiple of 600 seconds.

In the preferred version of the inventive method, the idiographic flow of step (2) is:

Utilize following formula to carry out resolution of vectors to the Monitoring Data of GPS displacement, obtain transversal displacement time-histories u _r(t):

u _r(t)=u _x(t)·sin(γ)-u _y(t)·cos(γ)

In formula, γ represents x axle in gps coordinate system and the angle of girder longitudinal axis;

Then L is divided into n 10 minutes sections, utilizes following formula to calculate u _r(t) mean value within each 10min time period, obtains horizontal quiet Displacement Sequence u _m(k):

$\mathrm{um}\left(k\right)=\left(\underset{t=600k-599}{\overset{t=600k}{\mathrm{\Σ}}}\mathrm{\μr}\left(t\right)\right)/600$

In formula, k is the sequence number of 10min time period, k=1, and 2 ..., n;

Finally utilize following formula to calculate laterally moving displacement time-histories u _d(t):

In formula,

represent t/600 to round up.

Beneficial effect: compared with prior art, the present invention has the following advantages:

1. in the time that definite girder laterally moves displacement, it is basis that the present invention proposes to utilize the true Monitoring Data of the GPS displacement components u (t) of the long-span bridges shown in step (1) under actual environment, and traditional theory derivation, finite element analogy and wind tunnel test are often similar to value and ignore minor effect factor as basis taking boundary condition supposition, initial parameter, the present invention more can determine the laterally moving displacement of long-span bridges girder truly, exactly by contrast;

2. in the time that definite girder laterally moves displacement, the present invention proposes the power spectrum of laterally moving displacement by the non-remarkable frequency band district f shown in step (3) ₁with remarkable frequency band district f ₂divide and carry out respectively Gauss curve fitting, can more accurately determine power spectral density plot, compared with determining method with traditional power spectral density plot, the present invention can more accurately utilize the harmonic wave method of superposition shown in step (4) to determine the laterally moving displacement of long-span bridges girder;

Therefore, the present invention can determine the laterally moving displacement of long-span bridges main beam member more truly, exactly, and the present invention can carry out laterally time-histories simulation and the prediction of extremum analysis of moving displacement of girder in subsequent applications, will obtain extensive promotion and application in the laterally moving Displacement Analysis field of long-span bridges main beam member.

Brief description of the drawings

Fig. 1 is embodiment of the present invention GPS displacement monitoring instrument equipment layout;

Fig. 2 is the horizontal quiet Displacement Sequence u of the embodiment of the present invention _m(k);

Fig. 3 is laterally moving displacement time-histories u of the embodiment of the present invention _d(t);

Fig. 4 is the laterally power spectrum density P (f) of moving displacement data of the embodiment of the present invention;

Fig. 5 is the non-remarkable frequency band district f of embodiment of the present invention power spectrum density P (f) ₁;

Fig. 6 is the remarkable frequency band district f of embodiment of the present invention power spectrum density P (f) ₂;

Fig. 7 is the non-remarkable frequency band district f of the embodiment of the present invention ₁power spectrum density fitting function

Fig. 8 is the remarkable frequency band district f of the embodiment of the present invention ₂power spectrum density fitting function

Fig. 9 is the laterally power spectrum density fitting function of moving displacement data of the embodiment of the present invention

Figure 10 be embodiment of the present invention q while getting 40000 parts girder laterally moving displacement time-histories in intraday matching time-histories;

Figure 11 be embodiment of the present invention q while getting 80000 parts girder laterally moving displacement time-histories in intraday matching time-histories;

Figure 12 be embodiment of the present invention q while getting 160000 parts girder laterally moving displacement time-histories in intraday matching time-histories;

Figure 13 is embodiment of the present invention q laterally power spectrum density of moving displacement matching time-histories in a day of girder while getting 40000 parts;

Figure 14 is embodiment of the present invention q laterally power spectrum density of moving displacement matching time-histories in a day of girder while getting 80000 parts;

Figure 15 is embodiment of the present invention q laterally power spectrum density of moving displacement matching time-histories in a day of girder while getting 160000 parts.

Embodiment

Below with reference to accompanying drawings, technical scheme of the present invention is described in detail.

A kind of definite long-span bridges girder of the present invention is the method for moving displacement laterally, comprises the steps:

Step (1): the Monitoring Data that gathers girder span centre GPS displacement:

GPS displacement monitoring station is installed at the girder span centre place of Loads of Long-span Bridges, motion vector u (t) is herein carried out to Real-Time Monitoring and with time series storage, u (t)=[u _x(t), u _y(t), u _z(t)], u _x(t), u _y(t), u _z(t) be respectively three direction of principal axis displacements under gps coordinate system, t represents the time, t=1, and 2 ..., L, unit is second, L represents time span;

Step (2): Monitoring Data is carried out to resolution of vectors and average value processing, laterally moved displacement data, idiographic flow is:

Utilize following formula to carry out resolution of vectors to the Monitoring Data of GPS displacement, obtain transversal displacement time-histories u _r(t):

u _r(t)=u _x(t)·sin(γ)-u _y(t)·cos(γ) （1）

In formula, γ represents x axle in gps coordinate system and the angle of girder longitudinal axis;

Then L is divided into n 10 minutes sections, utilizes following formula to calculate u _r(t) mean value within each 10min time period, obtains horizontal quiet Displacement Sequence u _m(k):

$\mathrm{um}\left(k\right)=\left(\underset{t=600k-599}{\overset{t=600k}{\mathrm{\Σ}}}\mathrm{\μr}\left(t\right)\right)/600---\left(2\right)$

In formula, k is the sequence number of 10min time period, k=1, and 2 ..., n, for ensureing that L can be divided into integer by 10 minutes sections, L should be the integral multiple of 600 seconds;

Utilize following formula to calculate laterally moving displacement components u _d(t):

In formula,

represent t/600 to round up, be used for judging which 10min time period time t drops in;

Due in each 10 minutes sections, there are 600 u _r(t) value, so the laterally moving displacement components u in each 10 minutes sections _d(t) be by the transversal displacement measured value u in this 10 minutes section _r(t) mean value that deducts all transversal displacement measured values in this 10 minutes section obtains;

Step (3): utilize the laterally power spectrum density of moving displacement data of Gauss's progression matching:

(a) first utilize and improve the laterally moving displacement time-histories u of period map method calculating _d(t) power spectrum density P (f), wherein f represents frequency values, P represents spectral density value, then draws power spectral density plot taking f, P as horizontal, ordinate respectively;

Time span L value is larger, utilizes and improves the laterally moving displacement components u of period map method calculating _d(t) power spectrum density P (f) is all the more stable, and therefore the time span L in step (1) at least should be 1 day;

(b) utilize the Peak Intensity Method of power spectrum density from power spectral density plot, determine non-remarkable frequency band district and be designated as f ₁, described non-remarkable frequency band district f ₁power spectrum density corresponding in power spectral density plot is designated as P ₁, described f ₁with P ₁one-to-one relationship in power spectral density plot adopts P ₁(f ₁) represent;

(c) utilize the Peak Intensity Method of power spectrum density from power spectral density plot, determine remarkable frequency band district and be designated as f ₂, remarkable frequency band district f ₂power spectrum density corresponding in power spectral density plot is designated as P ₂, f ₂with P ₂one-to-one relationship in power spectral density plot adopts P ₂(f ₂) represent;

(d) to non-remarkable frequency band district f ₁and corresponding power spectrum density P ₁carry out 4 rank Gaus series expressions matchings, determine the power spectrum density fitting function of non-remarkable frequency band district f1

idiographic flow is:

D1) by f ₁with P ₁get respectively denary logarithm, and 4 rank Gaus series expressions shown in substitution following formula:

$1g\left(P_1\right)=\underset{p=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\λ}}_p{e}^{-{\left(\frac{1g\left(f_1\right)-{\mathrm{\α}}_p}{{\mathrm{\β}}_p}\right)}^2}---\left(4\right)$

In formula, λ _p, α _pand β _pfor Gaussian parameter, p is the discrete variable of 4 rank Gauss's progression, p=1,2,3,4, lg (f ₁) and lg (P ₁) represent respectively f ₁with P ₁denary logarithm;

D2) the Gaussian parameter λ to 4 rank Gaus series expressions _p, α _pand β _pcarry out least square fitting, draw respectively and λ _p, α _pand β _pcorresponding best Gaussian parameter value

with

D3) utilize following formula to obtain non-remarkable frequency band district f ₁power spectrum density fitting function

${\hat{P}}_1\left(f_1\right)=10^{\left(\underset{p=1}{\overset{4}{\mathrm{\Σ}}}{\widehat{\mathrm{\λ}}}_p{e}^{-{\left(\frac{1g\left(f_1\right)-{\widehat{\mathrm{\α}}}_p}{{\widehat{\mathrm{\β}}}_p}\right)}^2}\right)---\left(5\right)}$

(e) to remarkable frequency band district f ₂and corresponding power spectrum density P ₂carry out the Gaus series expressions matching of (3+s) rank, determine remarkable frequency band district f ₂power spectrum density fitting function

wherein s is remarkable frequency band district f ₂the total number of spectral density peak value, idiographic flow is:

E1) by f ₂with P ₂get respectively denary logarithm, (3+s) rank Gaus series expressions shown in substitution following formula:

$1g\left(P_2\right)=\underset{m=1}{\overset{3+s}{\mathrm{\Σ}}}{a}_m{e}^{-{\left(\frac{1g\left(f_2\right)-b_m}{c_m}\right)}^2}---\left(6\right)$

In formula, a _m, b _mand c _mfor Gaussian parameter, m is the discrete variable of (3+s) rank Gauss's progression, m=1, and 2 ..., 3+s, lg (f ₂) and lg (P ₂) represent respectively f ₂with P ₂denary logarithm;

E2) the Gaussian parameter a to (3+s) rank Gaus series expressions _m, b _mand c _mcarry out least square fitting, draw respectively and a _m, b _mand c _mcorresponding best Gaussian parameter value

with

E3) utilize following formula to obtain remarkable frequency band district f ₂power spectrum density fitting function

${\hat{P}}_2\left(f_2\right)=10^{\left(\underset{m=1}{\overset{3+s}{\mathrm{\Σ}}}{a}_m{e}^{-{\left(\frac{1g(f_2-b_m)}{c_m}\right)}^2}\right)}---\left(7\right)$

Between step (d) and step (e), it is coordination;

(f) utilize the laterally power spectrum density of moving displacement data of Gauss's progression matching

employing following formula represents:

Step (4): utilize harmonic wave method of superposition to obtain laterally moving displacement match value of girder:

First by frequency f at frequency separation [f _minf _max] on be evenly divided into q part, obtain every part of frequency band length l and be:

$l=\frac{f_{\max }-f_{\min }}{q}---\left(9\right)$

In formula, f _maxfor the maximal value of frequency f, f _minfor the minimum value of frequency f, q is total umber of frequency band length, and q is larger, and laterally moving displacement is more accurate to utilize the definite girder of harmonic wave method of superposition, and therefore q at least should be greater than 20000 parts;

Then utilize following formula to calculate every part of centre frequency that frequency band length l is corresponding

${\tilde{f}}_j=l\·(j-0.5)---\left(10\right)$

In formula, j is the sequence number of every part of frequency band length, j=1, and 2 ..., q,

represent centre frequency corresponding to j part frequency band length l;

Harmonic wave superpositing function shown in recycling following formula obtains the laterally moving displacement match value of girder in any t moment

${\tilde{u}}_d\left(t\right)=\underset{j=1}{\overset{q}{\mathrm{\Σ}}}\sqrt{2\hat{P}\left({\tilde{f}}_j\right)\·l}\sin (2\mathrm{\π}{\tilde{f}}_{j}t+{\mathrm{\θ}}_j)---\left(11\right)$

In formula, θ _jfor obey j random sampling value of even stochastic distribution on [0,2 π] interval,

for in centre frequency

under the laterally power spectrum density of moving displacement data of Gauss's progression matching.

Laterally move Displacement Analysis as example taking the girder of the logical bridge of reviving below, specific embodiment of the invention process is described.

(1) the logical bridge of Soviet Union be connect Nantong and two cities, Zhenjiang across the Yangtze Bridge, employing double tower double plane cable stayed bridge structural system, wherein main beam member adopts streamlined Plate of Flat Steel Box Girder form, main span part longitudinal design size reaches 1088m.Based on bridge health monitoring system, based on step (1), the GPS displacement response at girder span centre position is carried out to long term monitoring and data acquisition, concrete monitoring instrument is arranged as shown in Figure 1, instrument sample frequency is all set as 1Hz, chooses the GPS displacement monitoring data on August 1st, 2012 to August 31;

(2) formula (1) based in step (2) is carried out resolution of vectors to Monitoring Data and is obtained transversal displacement time-histories u _r(t);

(3), utilize the formula (2) in step (2) to calculate u _r(t) mean value within each 10min time period, obtains horizontal quiet Displacement Sequence u _m(k), as shown in Figure 2;

(4) utilize the formula (3) in step (2) to calculate laterally moving displacement time-histories u _d(t), as shown in Figure 3;

(5) improve period map method based on (a) step utilization in step (3) and calculate the power spectrum density P (f) that laterally moves displacement data, as shown in Figure 4;

(6) utilize (b) step in step (3) and (c) step to determine the non-remarkable frequency band district f of power spectrum density P (f) ₁with remarkable frequency band district f ₂, respectively as shown in Figure 5 and Figure 6;

(7) utilize (d) step in step (3) to determine the power spectrum density fitting function of non-remarkable frequency band district f1 as shown in Figure 7, power spectrum density fitting function

best Gauss estimation of parameter value as shown in table 1;

Table 1 fitting function

best Gauss estimation of parameter value

(8) utilize (e) step in step (3) to determine remarkable frequency band district f ₂power spectrum density fitting function

as shown in Figure 8, power spectrum density fitting function

best Gauss estimation of parameter value as shown in table 2;

Table 2 fitting function

best Gauss estimation of parameter value

(9) utilize the formula (8) in step (3) to determine the power spectrum density fitting function that laterally moves displacement data

as shown in Figure 9, can find out with Fig. 4 contrast

can reflect preferably the power spectrum density P (f) of the laterally moving displacement of actual measurement;

(10) based on step (4), get respectively q=40000,80000 and 160000 parts, utilize harmonic wave method of superposition to determine laterally moving displacement time-histories of girder, its matching time-histories of a day as shown in Figure 10～Figure 12;

(11) utilize improve period map method calculate q=40000,80000 and 160000 parts of corresponding girders laterally the power spectrum density of moving displacement matching time-histories in a day respectively as shown in Figure 13～15, compared with the power spectrum density P (f) that laterally moves displacement data with actual measurement, the power spectrum density that can find out matching time-histories can reflect measured power spectral density preferably, has verified laterally accuracy and the validity of moving displacement method of a kind of definite long-span bridges girder that the present invention proposes.

Above embodiment is only further illustrating the present invention program; after having read the embodiment of the present invention, the amendment of those of ordinary skill in the art to various equivalents of the present invention and replacing all belongs to the scope of the protection that the present patent application claim limits.

Claims (3)

1. a laterally method for moving displacement of definite long-span bridges girder, is characterized in that, the method comprises the steps:

Step (1): the Monitoring Data that gathers girder span centre GPS displacement:

GPS displacement monitoring station is installed at the girder span centre place of Loads of Long-span Bridges, motion vector u (t) is herein carried out to Real-Time Monitoring and with time series storage, u (t)=[u _x(t), u _y(t), u _z(t)], u _x(t), u _y(t), u _z(t) be respectively three direction of principal axis displacements under gps coordinate system, t represents the time, t=1, and 2 ..., L, unit is second, L represents time span;

Step (2): Monitoring Data is carried out to resolution of vectors and average value processing, laterally moved displacement time-histories u _d(t);

Step (3): utilize the laterally power spectrum density of moving displacement data of Gauss's progression matching:

(a) first utilize and improve the laterally moving displacement time-histories u of period map method calculating _d(t) power spectrum density P (f), wherein f represents frequency values, P represents spectral density value, then draws power spectral density plot taking f, P as horizontal, ordinate respectively;

(b) utilize the Peak Intensity Method of power spectrum density from described power spectral density plot, determine non-remarkable frequency band district and be designated as f ₁, described non-remarkable frequency band district f ₁power spectrum density corresponding in power spectral density plot is designated as P ₁, described f ₁with P ₁one-to-one relationship in power spectral density plot adopts P ₁(f ₁) represent;

(c) utilize the Peak Intensity Method of power spectrum density from power spectral density plot, determine remarkable frequency band district and be designated as f ₂, remarkable frequency band district f ₂power spectrum density corresponding in power spectral density plot is designated as P ₂, f ₂with P ₂one-to-one relationship in power spectral density plot adopts P ₂(f ₂) represent;

(d) to non-remarkable frequency band district f ₁and corresponding power spectrum density P ₁carry out 4 rank Gaus series expressions matchings, determine non-remarkable frequency band district f ₁power spectrum density fitting function

idiographic flow is:

D1) by f ₁with P ₁get respectively denary logarithm, and 4 rank Gaus series expressions shown in substitution following formula:

$1g\left(P_1\right)=\underset{p=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\λ}}_p{e}^{-{\left(\frac{1g\left(f_1\right)-{\mathrm{\α}}_p}{{\mathrm{\β}}_p}\right)}^2}$

In formula, λ _p, α _pand β _pfor Gaussian parameter, p is the discrete variable of 4 rank Gauss's progression, p=1,2,3,4, lg (f ₁) and lg (P ₁) represent respectively f ₁with P ₁denary logarithm;

D2) the Gaussian parameter λ to 4 rank Gaus series expressions _p, α _pand β _pcarry out least square fitting, draw respectively and λ _p, α _pand β _pcorresponding best Gaussian parameter value

with

D3) utilize following formula to obtain non-remarkable frequency band district f ₁power spectrum density fitting function

${\hat{P}}_1\left(f_1\right)=10^{\left(\underset{p=1}{\overset{4}{\mathrm{\Σ}}}{\widehat{\mathrm{\λ}}}_p{e}^{-{\left(\frac{1g\left(f_1\right)-{\widehat{\mathrm{\α}}}_p}{{\widehat{\mathrm{\β}}}_p}\right)}^2}\right)}$

(e) to remarkable frequency band district f ₂and corresponding power spectrum density P ₂carry out the Gaus series expressions matching of (3+s) rank, determine remarkable frequency band district f ₂power spectrum density fitting function

wherein s is remarkable frequency band district f ₂the total number of spectral density peak value, idiographic flow is:

E1) by f ₂with P ₂get respectively denary logarithm, and (3+s) rank Gaus series expressions shown in substitution following formula:

$1g\left(P_2\right)=\underset{m=1}{\overset{3+s}{\mathrm{\Σ}}}{a}_m{e}^{-{\left(\frac{1g\left(f_2\right)-b_m}{c_m}\right)}^2}$

In formula, a _m, b _mand c _mfor Gaussian parameter, m is the discrete variable of (3+s) rank Gauss's progression, m=1, and 2 ..., 3+s, lg (f ₂) and lg (P ₂) represent respectively f ₂with P ₂denary logarithm;

E2) the Gaussian parameter a to (3+s) rank Gaus series expressions _m, b _mand c _mcarry out least square fitting, draw respectively and a _m, b _mand c _mcorresponding best Gaussian parameter value with

E3) utilize following formula to obtain remarkable frequency band district f ₂power spectrum density fitting function

${\hat{P}}_2\left(f_2\right)=10^{\left(\underset{m=1}{\overset{3+s}{\mathrm{\Σ}}}{a}_m{e}^{-{\left(\frac{1g(f_2-b_m)}{c_m}\right)}^2}\right)}$

(f) obtain utilizing the laterally power spectrum density of moving displacement data of Gauss's progression matching

be shown below:

Step (4): utilize harmonic wave method of superposition to obtain laterally moving displacement match value of girder:

By frequency f at frequency separation [f _minf _max] on be evenly divided into q part, obtain every part of frequency band length l and be:

$l=\frac{f_{\max }-f_{\min }}{q}$

In formula, f _maxfor the maximal value of frequency f, f _minfor the minimum value of frequency f, q is total umber of frequency band length;

Utilize following formula to calculate every part of centre frequency that frequency band length l is corresponding

${\tilde{f}}_j=l\·(j-0.5)$

In formula, j is the sequence number of every part of frequency band length, j=1, and 2 ..., q,

represent centre frequency corresponding to j part frequency band length l;

Utilize the harmonic wave superpositing function shown in following formula to obtain the laterally moving displacement match value of girder in any t moment

${\tilde{u}}_d\left(t\right)=\underset{j=1}{\overset{q}{\mathrm{\Σ}}}\sqrt{2\hat{P}\left({\tilde{f}}_j\right)\·l}\sin (2\mathrm{\π}{\tilde{f}}_{j}t+{\mathrm{\θ}}_j)$

In formula, θ _jfor obey j random sampling value of even stochastic distribution on [0,2 π] interval,

for in centre frequency

under the laterally power spectrum density of moving displacement data of Gauss's progression matching.

2. the method that the horizontal off-position of a kind of definite long-span bridges girder as claimed in claim 1 moves, is characterized in that, the time span L in described step (1) is at least 1 day, and is the integral multiple of 600 seconds.

3. the method that the horizontal off-position of a kind of definite long-span bridges girder as claimed in claim 1 or 2 moves, is characterized in that, the idiographic flow of described step (2) is:

Utilize following formula to carry out resolution of vectors to the Monitoring Data of GPS displacement, obtain transversal displacement time-histories u _r(t):

u _r(t)=u _x(t)·sin(γ)-u _y(t)·cos(γ)

In formula, γ represents x axle in gps coordinate system and the angle of girder longitudinal axis;

Then L is divided into n 10 minutes sections, utilizes following formula to calculate u _r(t) mean value within each 10min time period, obtains horizontal quiet Displacement Sequence u _m(k):

$\mathrm{um}\left(k\right)=\left(\underset{t=600k-599}{\overset{t=600k}{\mathrm{\Σ}}}\mathrm{\μr}\left(t\right)\right)/600$

In formula, k is the sequence number of 10min time period, k=1, and 2 ..., n;

Finally utilize following formula to calculate laterally moving displacement time-histories u _d(t):

In formula,

represent t/600 to round up.

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