CN106650221A - Method for enhancing bridge health monitoring structural response and temperature data correlation convergence - Google Patents

Abstract

The invention discloses a method for enhancing bridge health monitoring structural response and temperature data correlation convergence. The method comprises the steps that 1, bridge health monitoring system temperature data and corresponding structural response data in time are obtained; 2, a best-smooth algorithm is utilized for conducting smooth treatment on monitoring data; 3, the influence of a monitoring data time-lag effect on data correlation is eliminated by using a Fourier series theory, and meanwhile the dispersing action of frequency components of two data signals on a correlation relationship is reduced; 4, a multiple linear regression method is adopted for calculating an equivalent temperature and calculating a correlation coefficient between the structural response data and equivalent temperature data after time lag eliminating. Accordingly, the influence of factors such as data random fluctuation, the time-delay effect and the frequency components on the correlation coefficient can be effectively eliminated, and therefore convergence of correlation between the bridge health monitoring system structural response and the temperature data is enhanced, and great significance in bridge health monitoring early warning and evaluation is achieved.

Description

The method for strengthening bridge health monitoring structural response and the convergence of temperature data correlation

Technical field

The invention belongs to bridge health monitoring data dependence analysis research field, is related to bridge knot under a kind of temperature action Structure responds correlation analysis.

Background technology

Bridge health monitoring system data dependence analysis are the important contents of analysis of bridge structure research, and environmental load is One of bridge structure primary load.Temperature load specificity analysis is bridge structure design, construction, the important process of operation.Temperature Structural response property analysis associated therewith under effect, the inherent law that can be met with a response under temperature load effect, to bridge The assessment and early warning of structure has great significance.Environmental load has very strong regularity, in the case where weather is good, one As ' class sinusoidal ' type variation tendency is presented, many construction geometry linear change Monitoring Datas (such as amount of deflection, displacement, inclination angle) are in temperature There is more obvious dependency relation under degree effect.

Recently as the development of Bridge Health Monitoring Technology, health monitoring systems are widely used and bridge structure, because And can be with structural response data of the direct access bridge in the case where measured load is acted on so as to being prevented effectively from traditional theory deduction, having There is initial parameter assignment deviation, initial boundary conditions setting deviation and minor effect factor in the simulation of limit unit and wind tunnel test The incorrect problem ignored.But at present, to being temperature dependent property of structural response influence factor and how to cut down dry both at home and abroad Disturb and obtain the research work deficiency for more restraining correlative relationship.The true relevance rule of structural elements response under temperature action Still it is unknown, can eliminate or reduce the effective ways for being permitted correlation between Monitoring Data point interference in the urgent need to a kind of.

The content of the invention

Goal of the invention：The present invention provides one kind and can effectively eliminate Monitoring Data time-lag effect and reduce difference on the frequency between data The different impact to correlation, finally gives good dependency relation between equivalent temperature and structural response, more efficiently and effectively strengthens Bridge health monitoring structural response and the method for temperature data correlation convergence.

Technical scheme：The method for strengthening bridge health monitoring structural response and the convergence of temperature data correlation of the present invention, Comprise the following steps：

The first step：Obtain health monitoring systems temperature data and its in time corresponding structural response data, including knot Structure response data time series f_sr, temperature data time series x_{Ij i=1,2 ..., m, j=1,2 ... n}, wherein, i represents that sensor is compiled Number, j represents data length, and m is the bar number of time course data, and n is the number of every time course data；

Second step：Cut down algorithm respectively to health monitoring systems temperature data using best-smooth data fluctuations f_tempWith corresponding structural response data f_srSmooth treatment is carried out, the temperature data f after smooth treatment is obtained_{Temp, smooth}And structure Response data f_{Sr, smooth}；

3rd step：Time-lag effect is eliminated using Fourier space and reduce frequency difference to correlative relationship between Monitoring Data Impact, idiographic flow is：

(1) first by Fourier space to data f that obtain in second step_{Sr, smooth}, f_{Temp, smooth}Enter line frequency point Solution, obtains frequency data signal composition parameter, and idiographic flow is：

1) initial parameter u is calculated according to following formula₁With interim parameter u₂：

I=2p, 2p-1,2n-2 ... 2,1

Wherein,f_iData are represented in λ_iThe value at place, λ_iFor Data Position, k is sinusoidal signal Exponent number；

2) the cosine coefficient a of Fourier's factor is calculated according to following formula_kWith sinusoidal coefficients b_k：

Wherein, f₁For the value of first data in numerical signal；

3) the corresponding phase of each order frequency is obtained according to following formula_k：

Wherein, a₀,a₁,a₂,...,a_kIt is respectively the cosine coefficient of f (λ) Fourier's factor, b₁,b₂,…,b_kIt is respectively f (λ) sinusoidal coefficients of Fourier's factor, f (λ) approaches expression formula, each rank amplitude of signal for smooth data-signal Fourier space Forφ_k=arctan (a_k/b_k), k=1,2,3 ...；

(2) structural response data f after smooth treatment are solved_{Sr, smooth}With the temperature data f after smooth treatment_{Temp, smooth} Between phase difference △ φ under each same frequency_i, idiographic flow is：

1) expression formula difference computation structure response data f is approached according to Fourier space_{Sr, smooth}Phase_{Sr, k}, temperature Data f_{Temp, smooth}Phase_{Temp, k}：

Structural response data f_{Sr, smooth}Fourier space approach expression formula and be：

Temperature data f_{Temp, smooth}Fourier space approach expression formula and be：

2) phase difference △ φ are calculated according to following formula_i：

△φ_i=φ_temp,i-φ_sr,i, i=1,2,3 ..., k

Wherein, φ_temp,iFor i rank temperature data phase places, φ_sr,iFor i stage structure response data phase places；

(3) the minimal order k of Fourier expansion is determined_min, and calculate the structural response data after elimination time-lag effect f_{Sr, deltime-leg}, idiographic flow is：

1) Fourier expansion value f of computation structure data_fourierWith data smooth treatment value f_smoothBetween root mean squareBy RMSE<The 0.001 Fourier expansion minimal order for determining structural response data k_min；

2) phase place of each frequency content in structural response data Fourier space is converted into into temperature signal phase place, i.e., Translation △ φ_iPhase place, then by following formula to translating △ φ_iStructural response data after phase place are processed, and be eliminated time lag Structural response data f afterwards_{Sr, deltime-leg}：

Wherein, a_sr,0For the cosine coefficient of Fourier's factor of structural response data, c_sr,kIt is to eliminate structure after time-lag effect The amplitude of k ranks sinusoidal signal in response data Fourier expansion formula；

4th step：Calculate equivalent temperature data T and calculate and eliminate structural response data and temperature data after time-lag effect Between relative coefficient γ, idiographic flow is：

(1) delayed structural response data f when eliminating are obtained using multiple linear regression method_{Sr, deltime-leg}With m bars original temperature Time-histories Monitoring Data { x₁,x₂,x₃,...,x_mBetween best linear fit parameter b₀,b₁,b₂,...,b_m, and disappeared according to following formula calculating Except when delayed structural response data f_{Sr, deltime-leg}Best-fit values f '_{Sr, deltime-leg}：

f′_{Sr, deltime-leg}=b₀+b₁x₁+b₂x₂+…+b_mx_m；

(2) equivalent temperature data T are calculated by following formula：

Wherein, x_m,jFor j-th data in the m article temperature data, b_mFor multiple linear regression parameter；

(3) the structural response data and the relative coefficient γ between temperature data eliminated after time-lag effect are calculated by following formula：

Wherein,The average of the structural response data after to eliminate time-lag effect,It is equal for equivalent temperature data Value.

Further, in the inventive method, the idiographic flow of second step is：

1) in health monitoring time course data f, i.e. structural response data f_srWith temperature data f_tempUpper is J (λ) plus length Window；

2) window is moved from the front to the back on time course data according to length J (λ), while using Gauss curve fitting function S (λ) carries out Gauss curve fittings more than three ranks to the individual data of J in window (λ), then determines optimal length function by following formula J_best(λ) with the optimal Gauss curve fitting function S of each section_best(λ)：

{J_best(λ), S_best(λ) }=min { e²(S, J)=E (λ, f) [f-S (λ/J (λ))]²}

Wherein, e²(S, J) is error expectation, and J (λ) is length of window, and S (λ) is data Gauss curve fitting function in window, λ For the position of time course data, by { J_best(λ), S_best(λ) data smoothing value f } is obtained_smooth, i.e. the smooth value of structural response data f_{Sr, smooth}With smooth value f of temperature data_{Temp, smooth}。

Further, in the inventive method, 1 the step of second step) in, the initial value of length J (λ) is set as treating smooth number According to 1/10th of length.

Beneficial effect：The present invention compared with prior art, with advantages below：

1st, the method proposes first the method for eliminating structure time-lag effect, and correlation is presented oval between reasonable dismissal data The reason for type is distributed, while the various numerical signal processing methods of first Application are eliminated or compared with Small Time Lag effect and difference on the frequency logarithm According to the impact of a correlation, so as to obtain the correlation property more restrained between health monitoring systems data.

2nd, correlation analysis lack reliable theoretical foundation and effectively between the structural response data under current temperature action Analysis method, causes and regular governed correlative relationship is can not find between many structural response data and temperature.The present invention is based on Fourier space principle, multiple linear regression are theoretical, using best-smooth, MLR scheduling algorithm, obtain structure linear response The correlative relationship more restrained between data and temperature data, therefore with very strong engineering and research application prospect.

3rd, major function programmed realization of the invention, easy to operate, with very strong practicality.According to actual prison Data are surveyed, the method can effectively eliminate Monitoring Data time-lag effect and reduce impact of the frequency difference to correlation between data, Finally give dependency relation good between equivalent temperature and structural response.Therefore, it can extensively application and health monitoring systems number According to correlation analysis.

Description of the drawings

Fig. 1 is embodiment of the present invention bridge mid-span deflection smooth treatment figure；

Fig. 2 is correlation comparison diagram before and after embodiment of the present invention Monitoring Data smooth treatment；

Fig. 3 is that embodiment of the present invention Monitoring Data eliminates correlation comparison diagram before and after time lag；

Fig. 4 is embodiment of the present invention amount of deflection and equivalent temperature data linear regression graph.

Specific embodiment

Below with reference to accompanying drawings, technical scheme is described in detail.

The method for strengthening bridge health monitoring system structural response and temperature dependency convergence of the present invention, including following step Suddenly：

The first step：Obtain health monitoring systems temperature data and its in time corresponding structural response data；

Structural response data time series adopt f_srRepresent, temperature data time series is adopted x_{Ij i=1,2 ..., m, j=1,2 ... n}Represent.Wherein, i represents sensor number, and j represents data length.

Second step：Cut down algorithm to Monitoring Data smooth treatment using best-smooth data fluctuations, obtain f_{Sr, smooth}, f_{Temp, smooth}。

3rd step：Time-lag effect is eliminated using Fourier space and reduce frequency difference to correlative relationship between Monitoring Data Impact, idiographic flow is：

(1) first by Fourier space to data f that obtain in second step_{Sr, smooth}, f_{Temp, smooth}Enter line frequency point Solution, obtains frequency data signal composition parameter, and idiographic flow is：

1) initial parameter u is calculated according to following formula₁With interim parameter u₂：

I=2p, 2p-1,2n-2 ... 2,1

Wherein,f_iData are represented in λ_iThe value at place, λ_iFor Data Position, k is sinusoidal signal Exponent number；

2) the cosine coefficient a of Fourier's factor is calculated according to following formula_kWith sinusoidal coefficients b_k：

Wherein, f₁For the value of first data in numerical signal；

3) the corresponding phase of each order frequency is obtained according to following formula_k：

Wherein, a₀,a₁,a₂,...,a_kIt is respectively the cosine coefficient of f (λ) Fourier's factor, b₁,b₂,…,b_kIt is respectively f (λ) sinusoidal coefficients of Fourier's factor, f (λ) approaches expression formula, each rank amplitude of signal for smooth data-signal Fourier space Forφ_k=arctan (a_k/b_k), k=1,2,3 ...；

(2) structural response data f after smooth treatment are solved_{Sr, smooth}With the temperature data f after smooth treatment_{Temp, smooth} Between phase difference △ φ under each same frequency_i, idiographic flow is：

1) expression formula difference computation structure response data f is approached according to Fourier space_{Sr, smooth}Phase_{Sr, k}, temperature Data f_{Temp, smooth}Phase_{Temp, k}：

Structural response data f_{Sr, smooth}Fourier space approach expression formula and be：

Temperature data f_{Temp, smooth}Fourier space approach expression formula and be：

2) phase difference △ φ are calculated according to following formula_i：

△φ_i=φ_temp,i-φ_sr,i, i=1,2,3 ..., k

Wherein, φ_temp,iFor i rank temperature data phase places, φ_sr,iFor i stage structure response data phase places；

(3) the minimal order k of Fourier expansion is determined_min, and calculate the structural response number after elimination time-lag effect According to f_{Sr, deltime-leg}：

1) Fourier expansion value f of computation structure data_fourierWith data smooth treatment value f_smoothBetween root mean squareBy RMSE<The 0.001 Fourier expansion minimal order for determining structural response data k_min；

2) phase place of each frequency content in structural response data Fourier space is converted into into temperature signal phase place, i.e., Translation △ φ_iPhase place, then by following formula to translating △ φ_iStructural response data after phase place are processed, and be eliminated time lag Structural response data f afterwards_{Sr, deltime-leg}：

Wherein, a_sr,0For the cosine coefficient of Fourier's factor of structural response data, c_sr,kIt is to eliminate structure after time-lag effect The amplitude of k ranks sinusoidal signal in response data Fourier expansion formula；

4th step：Calculate equivalent temperature data T and calculate and eliminate structural response data and temperature data after time-lag effect Between relative coefficient γ.

(1) set up and eliminate time-lag effect structural response data f_{Sr, deltime-leg}Return with the multiple linear of former temperature monitoring data Return model：

Eliminate time lag structural response data f_{Sr, deltime-leg}To temperature variable { x₁,x₂,x₃,...,x_mM unit linear regression Equation is：

B therein₀,b₁,b₂,...,b_mFor the least-squares estimation value of coefficient,For multiple linear equation recurrence Estimate.Can solve according to below equation group.

Wherein：

I, k=1,2 ..., m；i≠k

(2) according to multiple linear regression parameter b₀,b₁,b₂,...,b_mCalculate equivalent temperature and set up knot delayed during elimination Structure response data f_{Sr, deltime-leg}With the unary linear regression equation of equivalent temperature data T and calculate and eliminate the knot after time-lag effect Relative coefficient γ between structure response data and temperature data：

f′_sr=a₀+a₁T(x_j), j=1,2,3 ... n

Wherein, x_m,jFor j-th data in the m article temperature data, b_mFor multiple linear regression parameter, f '_srFor f_{Sr, deltime-leg}With equivalent temperature T (x_j) between linear fit value, a₀, a₁For linear fit parameter,During to eliminate Residual effect should after structural response data average,For equivalent temperature data mean value.| γ | is bigger, represents that correlation is more notable.

(1) combined Yangtze Bridge total length 4010.81m in Huang gang, wherein, combined highway and metro section total length 2566.135m is (containing oblique Draw the main bridge 1215m of bridge), span is arranged as：11×32.7m+1.7m+(81+243+567+243+81)m+1.7m+(40+56+40) m+26×32.7m.The main bridge of the combined Yangtze Bridge in Huang gang is the double rope face steel truss girder cable-stayed bridges of double tower, and pylon foundation is employed 31 3m large diameter bored piles, High-Rise Pile Cap Foundation；Bridge tower adopts H xoncrete structures, tower height 193.5m (to contain pedestal)； Main bridge steel truss girder, using double main truss N truss, is inverted trapezoidal new type section form wide at the top and narrow at the bottom, 4.6 ten thousand tons of full-bridge steel truss girder；Tiltedly Drag-line is space Shuan Suo faces, and using parallel steel wire rope, full-bridge amounts to 152, and wherein maximum specification is PESC7-475, Suo Changyue 296m, weighs about 47 tons certainly.

(1) the amount of deflection response Monitoring Data and corresponding temperature data acquisition based on step a pair of girder span centre position, instrument Device sample frequency is 1Hz.August in 2015 is chosen 16 to the August mid-span deflection of 18 days and temperature monitoring data analysis；

(2) temperature and deflection data smooth treatment based on step 2 to acquisition in step one, such as Fig. 1, shown in 2.

(3) Monitoring Data time-lag effect is eliminated based on step 3, as shown in Figure 3.Health monitoring amount of deflection and the smooth number of temperature 1 is shown in Table according to each rank phase difference of Fourier space.

15 order frequency parameters and its phase difference before the amount of deflection of table 1 and temperature monitoring data Fourier space

(4) equivalent temperature data T are calculated and is calculated based on step 4 and eliminate structural response data and temperature after time-lag effect Relative coefficient γ between degrees of data.

Using 4 temperature sensors of bridge span centre and amount of deflection Sensor monitoring data, by step 2, three when being eliminated Delayed amount of deflection time series, according to step 4 optimum regression model is obtained.

The temperature of table 2 and deflection monitoring data regression parameters

Calculate equivalent temperature:

One-variable linear regression relation is set up to equivalent temperature and the structural deflection data for eliminating time lag, as shown in Figure 4.And count Calculate and eliminate structural response data and the relative coefficient γ between temperature data after time-lag effect_deltime-leg=0.876 is significantly big Relative coefficient γ between prototype structure response data and temperature data_deltime-leg=0.412, checking the method fast has Effect.

Above-described embodiment is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill of the art For personnel, under the premise without departing from the principles of the invention, some improvement and equivalent can also be made, these are to the present invention Claim is improved and the technical scheme after equivalent, each falls within protection scope of the present invention.

Claims (3)

1. it is a kind of to strengthen the method that bridge health monitoring structural response and temperature data correlation restrain, it is characterised in that the party Method is comprised the following steps：

The first step：Health monitoring systems temperature data and its in time corresponding structural response data are obtained, including structure is rung Answer data time series f_sr, temperature data time series x_{Iji=1,2 ..., m, j=1,2 ... n}, wherein, i represents sensor number, j tables Show data length, m is the bar number of time course data, and n is the number of every time course data；

Second step：Cut down algorithm respectively to health monitoring systems temperature data f using best-smooth data fluctuations_tempWith it is right Structural response data f answered_srSmooth treatment is carried out, the temperature data f after smooth treatment is obtained_{Temp, smooth}With structural response number According to f_{Sr, smooth}；

3rd step：Time-lag effect is eliminated using Fourier space and reduce shadow of the frequency difference correlative relationship between Monitoring Data Ring, idiographic flow is：

(1) first by Fourier space to data f that obtain in the second step_{Sr, smooth}, f_{Temp, smooth}Enter line frequency point Solution, obtains frequency data signal composition parameter, and idiographic flow is：

1) initial parameter u is calculated according to following formula₁With interim parameter u₂：

$\left\{\begin{array}{c}{u}_{2p+2}=u_{2p+1}=0\\ u_i=f_i+2cos\left(kl\right)u_{i+1}-u_{i+2}\end{array}\right.$

I=2p, 2p-1,2n-2 ... 2,1

Wherein,f_iData are represented in λ_iThe value at place, λ_iFor Data Position, k is sinusoidal signal exponent number；

2) the cosine coefficient a of Fourier's factor is calculated according to following formula_kWith sinusoidal coefficients b_k：

$a_k=\frac{2}{2p+1}(f_1+u_{1}cos(k\mathrm{\&lambda;})-u_2)$

$b_k=\frac{2}{2p+1}+u_{1}sin\left(k\mathrm{\&lambda;}\right)$

Wherein, f₁For the value of first data in numerical signal；

3) the corresponding phase of each order frequency is obtained according to following formula_k：

$f_{fourier}=\frac{a_0}{2}+\underset{k=1}{\overset{\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{a}_k\cos \left(k\mathrm{\&lambda;}\right)+\underset{k=1}{\overset{\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{b}_k\sin \left(k\mathrm{\&lambda;}\right)=\frac{a_0}{2}+\underset{k=1}{\overset{\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{c}_k\sin (k\mathrm{\&lambda;}+{\mathrm{\&phi;}}_k)$

Wherein, a₀,a₁,a₂,...,a_kIt is respectively the cosine coefficient of f (λ) Fourier's factor, b₁,b₂,…,b_kIt is respectively Fu of f (λ) In the leaf factor sinusoidal coefficients, f (λ) approaches expression formula for smooth data-signal Fourier space, and each rank amplitude of signal isφ_k=arctan (a_k/b_k), k=1,2,3 ...；

(2) structural response data f after smooth treatment are solved_{Sr, smooth}With the temperature data f after smooth treatment_{Temp, smooth}Between it is each Phase difference △ φ under individual same frequency_i, idiographic flow is：

1) expression formula difference computation structure response data f is approached according to Fourier space_{Sr, smooth}Phase_sr,k, temperature data f_{Temp, smooth}Phase_temp,k：

Structural response data f_{Sr, smooth}Fourier space approach expression formula and be：

$f_{sr,fourier}=\frac{a_{sr,0}}{2}+\underset{k=1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{c}_{sr,k}sin({\mathrm{k\&lambda;}}_{sr}+{\mathrm{\&phi;}}_{sr,k})$

Temperature data f_{Temp, smooth}Fourier space approach expression formula and be：

$f_{temp,fourier}=\frac{a_{temp,0}}{2}+\underset{k=1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{c}_{temp,k}sin({\mathrm{k\&lambda;}}_{temp}+{\mathrm{\&phi;}}_{temp,k})$

2) phase difference △ φ are calculated according to following formula_i：

△φ_i=φ_temp,i-φ_sr,i, i=1,2,3 ..., k

Wherein, φ_temp,iFor i rank temperature data phase places, φ_sr,iFor i stage structure response data phase places；

(3) the minimal order k of Fourier expansion is determined_min, and calculate the structural response data after elimination time-lag effect f_{Sr, deltime-leg}, idiographic flow is：

1) Fourier expansion value f of computation structure data_fourierWith data smooth treatment value f_smoothBetween root mean squareBy RMSE<The 0.001 Fourier expansion minimal order for determining structural response data k_min；

2) phase place of each frequency content in structural response data Fourier space is converted into into temperature signal phase place, that is, is translated △φ_iPhase place, then by following formula to translating △ φ_iStructural response data after phase place are processed, delayed when being eliminated Structural response data f_{Sr, deltime-leg}：

$f_{sr,deltime-leg}=\frac{a_{sr,0}}{2}+\underset{i=1}{\overset{k_{\min }}{\&Sigma;}}{c}_{sr,i}sin(i\mathrm{\&lambda;}+{\mathrm{\&phi;}}_{temp,i})$

Wherein, a_sr,0For the cosine coefficient of Fourier's factor of structural response data, c_sr,iIt is to eliminate structural response after time-lag effect The amplitude of i ranks sinusoidal signal in data Fourier expansion formula；

4th step：Equivalent temperature data T are calculated, it is determined that eliminating structural response data and the phase between temperature data after time-lag effect Property coefficient γ is closed, idiographic flow is：

(1) delayed structural response data f when eliminating are obtained using multiple linear regression method_{Sr, deltime-leg}With m bars original temperature time-histories Monitoring Data { x₁,x₂,x₃,...,x_mBetween best linear fit parameter b₀,b₁,b₂,...,b_m, and when calculating elimination according to following formula Lag structure response data f_{Sr, deltime-leg}Best-fit values f '_{Sr, deltime-leg}：

f′_{Sr, deltime-leg}=b₀+b₁x₁+b₂x₂+…+b_mx_m；

(2) equivalent temperature data T are calculated by following formula：

$T=(b_1\&times;x_{1,j}+b_2\&times;x_{2,j}+...+b_m\&times;x_{m,j})/\underset{i=1}{\overset{m}{\&Sigma;}}{b}_i$

Wherein, x_m,jFor j-th data in the m article temperature data, b_mFor multiple linear regression parameter；

(3) the structural response data and the relative coefficient γ between temperature data eliminated after time-lag effect are calculated by following formula：

$\mathrm{\&gamma;}=coef(f_{sr,deltime-leg},T)=\frac{\mathrm{\&Sigma;}(f_{sr,deltime-leg}-{\stackrel{\&OverBar;}{f}}_{sr,deltime-leg})(T-\stackrel{\&OverBar;}{T})}{\sqrt{{(f_{sr,deltime-leg}-{\stackrel{\&OverBar;}{f}}_{sr,deltime-leg})}^2}\sqrt{{(T-\stackrel{\&OverBar;}{T})}^2}}$

Wherein,The average of the structural response data after to eliminate time-lag effect,For equivalent temperature data mean value.

It is 2. according to claim 1 to strengthen the method that bridge health monitoring structural response and temperature data correlation restrain, Characterized in that, the idiographic flow of the second step is：

1) in health monitoring time course data f, i.e. structural response data f_srWith temperature data f_tempThe upper window for adding length for J (λ) Mouthful；

2) window is moved from the front to the back on time course data according to length J (λ), while using Gauss curve fitting function S (λ) Gauss curve fittings more than three ranks is carried out to the individual data of J in window (λ), then optimal length function J is determined by following formula_best (λ) with the optimal Gauss curve fitting function S of each section_best(λ)：

{J_best(λ), S_best(λ) }=min { e²(S, J)=E (λ, f) [f-S (λ/J (λ))]²}

Wherein, e²(S, J) is error expectation, and J (λ) is length of window, and S (λ) is data Gauss curve fitting function in window, and λ is time-histories The position of data, by { J_best(λ), S_best(λ) data smoothing value f } is obtained_smooth, i.e. the smooth value of structural response data f_{Sr, smooth}With smooth value f of temperature data_{Temp, smooth}。

It is 3. according to claim 2 to strengthen the method that bridge health monitoring structural response and temperature data correlation restrain, Characterized in that, the step of second step 1) in, the initial value of length J (λ) be set as treating smooth data length ten/ One.