CN104297004A - Real-time bridge damage early-warning method based on AR-ARX model - Google Patents

Abstract

The invention relates to the technical field of bridge structure damage recognition and provides a real-time bridge damage early-warning method. The subjectivity of the method is reduced, the operability is high, the structure damage position and the damage degree can be effectively recognized, and the precision and the efficiency of damage early warning are improved. According to the technical scheme, the real-time bridge damage early-warning method based on an AR-ARX model comprises the following steps that 1), sensors are arranged on a target real bridge; 2), dynamic signals of real-time bridge monitoring under environmental motivation are obtained; 3), a normal state and an unknown state are selected; 4), standardization processing is carried out on all sample data; 5), an auto-regression AR model is set up, and coefficients of the AR model are utilized for carrying out data sample matching; 6), an auto-regression ARX model with external input is set up; 7), statistics assessment is carried out on DF values to determine statistical characteristic values PD; 8), threshold values for early warning are determined. The method is mainly used for bridge structure damage recognition.

Description

The real-time damage alarming method of bridge based on AR-ARX model

Technical field

The present invention relates to the technical field of Damage Identification of Bridge Structure, particularly a kind of real-time damage alarming method of structure based on time series models residual error.

Technical background

The high speed steady growth of development and improvement to national economy of communications and transportation cause plays a part great, and the normal operation of bridge structure is the prerequisite that traffic and transportation system runs well.Along with rising steadily of the volume of traffic, there is damaged phenomenon also in increase in structure, causes bridge capacity to decline, if can not identification of damage in time, makes it be accumulated to a certain degree, once destroy, bring great loss by society.Therefore, Study on Damage Identification is carried out to bridge, there is important theory significance and use value.

The structural healthy monitoring system of the Longspan Bridge that Present Domestic is existing and newly-built utilizes on-the-spot harmless sensing technology, obtain structure Real-Time Monitoring signal, research structure system performance is carried out, as based on natural frequency, Mode Shape, modal curvature, stiffness matrix, flexibility matrix and Modifying model etc. by the change of analytical structure physical parameter and structural dynamic feature.Therefore identification of damage can be carried out by analytical structure system performance.Such as, but said method has its limitation, for large bridge structure, high order mode is difficult to obtain; Mode Shape is measured imperfect; Measurement point needs optimum choice etc.

At present, the bridge damnification recognition method of structure based vibration characteristics exists that data volume is large, calculation of complex and the shortcoming such as non-destructive tests efficiency is not high, and depend critically upon sensor and interpretation algorithms in actual applications, the problem of effective damage alarming in real time can not be carried out.

Summary of the invention

, calculation of complex large for existing bridge damnification method for early warning data volume and the shortcoming such as identification of damage efficiency is not high, can not carry out the problem of effective damage alarming in real time.For overcoming the deficiencies in the prior art, there is provided a kind of bridge real-time damage alarming method, the defining method of Improving Working Timing model order, reduce its subjectivity, improve the efficiency of bridge real time health monitoring, simultaneously, the Information Condensing that a large amount of structural response data of Real-Time Monitoring can be contained is the model parameter of minority, workable, STRUCTURE DAMAGE LOCATION and degree of injury be can effectively identify, precision and the efficiency of damage alarming improved.For this reason, the technical scheme that the present invention takes is, based on autoregressive model and autoregressive model (the Autoregressive models-Autoregressive models with eXogenous inputs with outside input, be called for short AR-ARX model) the real-time damage alarming method of bridge, comprise the steps:

1) placement sensor on the real bridge of target;

2) Dynamic Signal of bridge Real-Time Monitoring under environmental excitation is obtained;

3) selected reference state and unknown state, is divided into different data sets the time-histories data data of different conditions, and generates multiple little data sample;

4) each sample data is carried out standardization;

5) set up autoregression (AR) model, utilize AR model coefficient to carry out data sample matching treatment;

6) set up autoregression (ARX) model with outside input, utilize ARX model residual computations every measuring point damage characteristic value DF;

7) statistical estimation determination statistical property value PD is carried out to DF value;

8) definite threshold, statistical property value PD exceedes threshold value and sends pre-alert notification, does not exceed threshold value, does not send pre-alert notification.

The Dynamic Signal of bridge Real-Time Monitoring under acquisition environmental excitation, specifically, according to nyquist sampling theorem determination sample frequency, obtains bridge Real-Time Monitoring acceleration signal.

Sample data carried out standardization pre-service before setting up AR model, and the method for employing is:

$\hat{x}\left(t\right)=\frac{x\left(t\right)-{\mathrm{\μ}}_x}{{\mathrm{\σ}}_x}$

In formula, x (t) is Real-Time Monitoring acceleration signal, for the signal after process, μ _xand σ _xthe average of difference x (t) and standard deviation.

The Optimization Steps of AR-ARX model order comprises:

A.AR model order is designated as p, and the order of ARX is designated as order=[n _a, n _b, n _k], wherein, n _aaR part order, n _boutside input order, n _kit is the pure delay time of system;

B. AR model order p is determined according to AIC criterion (AkaikeInformation Criterion);

C. at guarantee n _a+ n _b<p and n _a>n _bcondition under selected n _aand n _bvalue;

D.n _kvalue target be meet AIC criterion and that loss function value is got is minimum, determine n according to AIC criterion _kspan, counting loss functional value within the scope of this, the minimum order of loss function value is the ARX model order finally determined.

Consider coefficient and the residual error of AR model, propose Data Matching formula:

$\mathrm{Corr}=\frac{\left|({{\mathrm{\&sigma;}}_x}^2-{{\mathrm{\&sigma;}}_y}^2)\right|\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_x}^2\left(k\right)}\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_y}^2}}{\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_x\left(k\right)a_y\left(k\right)}$

In formula, σ _x ², σ _y ²for the variance of AR model residual error, a _x(k), a _yk () is AR model coefficient, get minimum value carry out matched data sample according to formula.

Residual error based on ARX model extracts damage characteristic value.

Carry out the non-destructive tests statistical estimation based on great amount of samples, draw the expression formula of damage probability.

Compared with the prior art, technical characterstic of the present invention and effect:

(1) based on time series analysis identification of damage, directly set up temporal model to time domain response data, model parameter contains a large amount of structural information, gets final product identification of damage by extracting damage sensitive features index, more simple and quick compared with modal parameter method.

(2), set up temporal model in analysis before, sample matches is carried out to the time domain response data gathered, reduces the impact of environment.

(3) this method is when setting up AR-ARX model, is optimized its Method of determining the optimum, reduces the subjectivity that model order is determined, improves non-destructive tests efficiency.

(4) situation for the single damage of structure and the damage of two places is analyzed by the method carried, can identification of damage position and degree of injury.

Accompanying drawing explanation

Fig. 1 Damage Alarming of Bridge Structures process flow diagram

Two span continuous beam models of Fig. 2 embodiment of the present invention and sensor are arranged

The simulation of damage regime in Fig. 3 embodiment of the present invention

In Fig. 4 embodiment of the present invention under DC11 operating mode the Acceleration time course of measuring point 3

(a) measuring point 2, (b) measuring point 6.

The non-destructive tests result of Fig. 5 embodiment of the present invention measuring point 2 and measuring point 6 under single injury operating mode

(a) measuring point 2; (b) measuring point 6.

The non-destructive tests result of Fig. 6 embodiment of the present invention measuring point 2 and measuring point 6 under two damage regime.

Embodiment

The technical solution used in the present invention is,

1., based on the real-time damage alarming method of bridge of AR-ARX model, comprise the steps:

1) placement sensor on the real bridge of target;

2) Dynamic Signal of bridge Real-Time Monitoring under environmental excitation is obtained;

3) selected reference state and unknown state, is divided into different data sets the time-histories data data of different conditions, and generates multiple little data sample;

4) each sample data is carried out standardization;

5) set up AR (Autoregressive models) model, utilize AR model coefficient to carry out data sample matching treatment;

6) set up ARX (Autoregressive models with eXogenous inputs) model, utilize ARX model residual computations every measuring point damage characteristic value DF;

7) statistical estimation determination statistical property value PD is carried out to DF value;

8) definite threshold, statistical property value PD exceedes threshold value and sends pre-alert notification, does not exceed threshold value, does not send pre-alert notification.

2. the signal adopted in bridge damnification method for early warning is acceleration signal.

3. when determining sample frequency, consider nyquist sampling theorem.

4. sample data carried out standardization pre-service before setting up temporal model, and the method for employing is:

$\hat{x}\left(t\right)=\frac{x\left(t\right)-{\mathrm{\&mu;}}_x}{{\mathrm{\&sigma;}}_x}$

In formula, x (t) is Real-Time Monitoring acceleration signal, for the signal after process, μ _xand σ _xthe average of difference x (t) and standard deviation.

The Optimization Steps of 5.AR-ARX model order comprises:

A.AR model order is designated as p, and the order of ARX is designated as order=[n _a, n _b, n _k], wherein, n _aaR part order, n _boutside input order, n _kit is the pure delay time of system;

B. AR model order p is determined according to AIC criterion (AkaikeInformation Criterion);

C. at guarantee n _a+ n _b<p and n _a>n _bcondition under selected n _aand n _bvalue;

D.n _kvalue target be meet AIC criterion and that loss function value is got is minimum, determine n according to AIC criterion _kspan, counting loss functional value within the scope of this, the minimum order of loss function value is the ARX model order finally determined.

6. consider circumstance complication residing for the bridge in actual operation, the dynamic response of bridge is affected by environment comparatively large, for reducing the impact of environment, considering coefficient and the residual error of AR model, proposing Data Matching formula:

$\mathrm{Corr}=\frac{\left|({{\mathrm{\&sigma;}}_x}^2-{{\mathrm{\&sigma;}}_y}^2)\right|\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_x}^2\left(k\right)}\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_y}^2}}{\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_x\left(k\right)a_y\left(k\right)}$

In formula, σ _x ², σ _y ²for the variance of AR model residual error, a _x(k), a _yk () is AR model coefficient, get minimum value carry out matched data sample according to formula.

7. the residual error based on ARX model extracts damage characteristic value.

8. carry out the non-destructive tests statistical estimation based on great amount of samples, draw the expression formula of damage probability.

The present invention is further described below in conjunction with accompanying drawing.

The present invention proposes a kind of bridge damnification method for early warning: the real-time damage alarming method of the bridge based on AR-ARX model.Composition graphs 1, its feature comprises the following steps:

(1) according to nyquist sampling theorem determination sample frequency, obtain bridge Real-Time Monitoring acceleration signal x (t), t is time variable.Front t ₀acceleration responsive in moment is normal condition signal x ₀t (), is divided into reference data set and lossless data collection, is designated as Set respectively ^rand Set ^h.Set ^rfor Data Matching, Set ^hfor setting up damage characteristic value.I-th monitoring periods t _ithe acceleration signal of time period is unknown state signal x _it (), wherein with Set ^hthe signal of equal length is unknown data collection, is designated as Set _i ^u.Set ^r, Set ^hand Set ^ube divided into again less data sample, consider the uncertainty of statistics, between adjacent data sample, have overlap.By following formula, standardization is carried out to all sample datas:

$\hat{x}\left(t\right)=\frac{x\left(t\right)-{\mathrm{\&mu;}}_x}{{\mathrm{\&sigma;}}_x}---\left(1\right)$

In formula, for the signal after process, μ _xand σ _xbe respectively average and the standard deviation of original signal x (t).

(2) for lossless data collection Set ^hwith unknown data collection Set _i ^uin each sample, at reference data set Set ^rin find a reference sample, form pair of sample group, both have similar environmental baseline.First to Set ^r, Set ^hand Set ^uin sample set up AR model respectively, AR model order p determines according to AIC criterion (AkaikeInformation Criterion).AR mould of setting up is:

$x\left(n\right)=-\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_x\left(k\right)x(n-k)+u_x\left(n\right)---\left(2\right)$

$y\left(n\right)=-\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_y\left(k\right)y(n-k)+u_y\left(n\right)---\left(3\right)$

In formula, x (n), y (n) are respectively Set ^r, Set ^h/ Set ^uin sample data, a _x(k), a _yk () is AR model coefficient, document has relevant record, and p is AR model order, u _x(n), u _yn () is AR model prediction residual error.Consider coefficient and the residual error of AR model, propose Data Matching formula, get minimum value according to formula (4) and carry out matched data sample.

$\mathrm{Corr}=\frac{\left|({{\mathrm{\&sigma;}}_x}^2-{{\mathrm{\&sigma;}}_y}^2)\right|\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_x}^2\left(k\right)}\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_y}^2}}{\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_x\left(k\right)a_y\left(k\right)}---\left(4\right)$

In formula, σ _x ², σ _y ²for the variance of AR model residual error, all the other parameters are such as formula (2) and formula (3).

(3) the residual error extraction damage characteristic value of ARX model is built based on sample institute that is harmless and unknown data collection.The ARX model set up is:

$x\left(n\right)=\underset{i=1}{\overset{n_a}{\mathrm{\&Sigma;}}}\&PartialD;\left(i\right)x(n-i)+\underset{i=1}{\overset{n_b}{\mathrm{\&Sigma;}}}\mathrm{\&beta;}\left(j\right)u_x(n-j)+{e_x}^{\&prime;}---\left(5\right)$

In formula, for ARX model prediction coefficient, ((i) is the predictive coefficient of ARX model external input part to β, u _x(n-j) for the outside of ARX model inputs, the AR model residual error namely determined by formula (2), e _xn () is the prediction residual of ARX model.If configuration state does not change, the ARX model prediction residual error that the sample of unknown data collection and lossless data collection is set up is by close.If damage appears in structure, the ARX model prediction residual error that the sample of unknown data collection is set up will increase.Damage characteristic value is defined as follows:

$D_F=\frac{{{\mathrm{\&sigma;}}_y}^2-{{\mathrm{\&sigma;}}_x}^2}{{{\mathrm{\&sigma;}}_x}^2}---\left(6\right)$

In formula, σ _x ², σ _y ²be respectively Set ^r, Set ^h/ Set ^uthe variance of the ARX model prediction residual error that middle matched sample group is set up.If change does not appear in configuration state, DF value should close to 0; If damage appears in structure, DF value should be greater than 0.

(4) the damage characteristic D that harmless and unknown data concentrates each measuring point place to calculate is supposed _f,Hand D _f,Unormal Distribution, X=D _f,H-D _f,Ualso Normal Distribution, derives D accordingly _f,Ube greater than D _f,Hthe probability expression of (namely damage appears in structure):

$P_D=\mathrm{\&Phi;}\left(\frac{m_U-m_H}{\sqrt{{{\mathrm{\&sigma;}}_U}^2+{{\mathrm{\&sigma;}}_H}^2}}\right)---\left(7\right)$

In formula, m _u, m _hthe average of each sensor place damage characteristic value under being respectively unknown state and nondestructive state, σ _u ², σ _h ²be respectively the variance of unknown state and nondestructive state next sensor place damage characteristic value.P _dlarger, show that structure occurs that the probability of damage is larger.

For making object of the invention process, technical scheme and advantage clearly, below in conjunction with accompanying drawing and a specific embodiment, further detailed description is done to the present invention, but this explanation can not be construed as limiting the invention.

For two across joist steel Continuous Beam Model, model general layout is as Fig. 2.Continuous beam overall length 6m, two across each 2.8m, and centre is fixed-hinged support, and both sides are movable hinged shoe.Adopt general finite meta software ansys to set up finite element model, select beam3 unit to simulate, divide 126 nodes altogether, 125 unit.Girder section Stiffness is realized by cutting flange plate.First damage position is left across span centre, and the edge of a wing, cross section cutting width is 2cm, and totally three kinds of operating modes, are designated as DC11, DC12 and DC13; Second damage position is right across span centre, and the edge of a wing, cross section cutting width is 10cm, and totally two kinds of operating modes, are designated as DC21 and DC22.Cut second damage position after first damage position reaches maximum degree of injury again, damage regime is arranged as Fig. 3.Fig. 4 is the Acceleration time course of measuring point 2 under DC11 operating mode in the embodiment of the present invention.

Fig. 5 is the DF value probability density function curve of matching under single injury operating mode, shown in Fig. 5 (a), each damage regime and harmless performance curve dispersion are comparatively large, show left across the existence damage of span centre place, and along with the increase of degree of injury, DF average increases gradually.Shown in Fig. 5 (b), do not establish the measuring point 8 place probability density function curve discrete degree of damage little compared with measuring point 2, average difference is not obvious.As seen from Figure 6, probability density function curve and the harmless operating mode of measuring point 2 and each damage regime of measuring point 6 are obviously different, show right across the existence damage of span centre place.Calculate the PD value of each measuring point, in table 1.Under single injury operating mode, the PD value of measuring point 2 is all greater than 90%, and all the other are all less than 80%.Under two damage regime, the PD value of measuring point 2 and measuring point 6 is also all greater than 90%.But under DC22 operating mode, the PD value of measuring point 3 and measuring point 5 is respectively 89.4% and 87.5%.Institute's optimization method can identification of damage position and degree of injury, and phenomenon of not failing to judge, although sometimes may cause erroneous judgement, but still can orient damage field roughly.

The P of each measuring point of table 1 _dvalue (%)

Claims (6)

1., based on the real-time damage alarming method of bridge of AR-ARX model, it is characterized in that, comprise the following steps:

1) placement sensor on the real bridge of target;

2) Dynamic Signal of bridge Real-Time Monitoring under environmental excitation is obtained;

3) selected reference state and unknown state, is divided into different data sets the time-histories data data of different conditions, and generates multiple little data sample;

4) each sample data is carried out standardization;

5) set up autoregressive model-AR model (Autoregressive models), utilize AR model coefficient to carry out data sample matching treatment;

6) set up the autoregressive model-ARX model (Autoregressive models with eXogenous inputs) with outside input, utilize ARX model residual computations every measuring point damage characteristic value DF;

7) statistical estimation determination statistical property value PD is carried out to DF value;

8) definite threshold, statistical property value PD exceedes threshold value and sends pre-alert notification, does not exceed threshold value, does not send pre-alert notification.

2. as claimed in claim 1 based on the real-time damage alarming method of bridge of AR-ARX model, it is characterized in that, the Dynamic Signal of bridge Real-Time Monitoring under acquisition environmental excitation, specifically, according to nyquist sampling theorem determination sample frequency, obtain bridge Real-Time Monitoring acceleration signal.

3., as claimed in claim 1 based on the real-time damage alarming method of bridge of AR-ARX model, it is characterized in that, sample data carried out standardization pre-service before setting up AR model, and the method for employing is:

$\hat{x}\left(t\right)=\frac{x\left(t\right)-{\mathrm{\&mu;}}_x}{{\mathrm{\&sigma;}}_x}$

In formula, x (t) is Real-Time Monitoring acceleration signal, for the signal after process, μ _xand σ _xbe respectively average and the standard deviation of x (t).

4., as claimed in claim 1 based on the real-time damage alarming method of bridge of AR-ARX model, it is characterized in that, the Optimization Steps of AR-ARX model order comprises:

A.AR model order is designated as p, and the order of ARX is designated as order=[n _a, n _b, n _k], wherein, n _aaR part order, n _boutside input order, n _kit is the pure delay time of system;

B. AR model order p is determined according to AIC (AkaikeInformation Criterion) criterion;

C. at guarantee n _a+ n _b<p and n _a>n _bcondition under selected n _aand n _bvalue;

D.n _kvalue target be meet AIC criterion and that loss function value is got is minimum, determine n according to AIC criterion _kspan, counting loss functional value within the scope of this, the minimum order of loss function value is the ARX model order finally determined.

Consider coefficient and the residual error of AR model, propose Data Matching formula:

$\mathrm{Corr}=\frac{\left|({{\mathrm{\&sigma;}}_x}^2-{{\mathrm{\&sigma;}}_y}^2)\right|\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_x}^2\left(k\right)}\sqrt{{\mathrm{\&Sigma;}}_{k=1}^p{a_y}^2}}{\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_x\left(k\right)a_y\left(k\right)}$

In formula, σ _x ², σ _y2 is the variance of AR model residual error, a _x(k), a _yk () is AR model coefficient, get minimum value carry out matched data sample according to formula.

5. as claimed in claim 1 based on the real-time damage alarming method of bridge of AR-ARX model, it is characterized in that, the residual error based on ARX model extracts damage characteristic value.

6., as claimed in claim 1 based on the real-time damage alarming method of bridge of AR-ARX model, it is characterized in that, carry out the non-destructive tests statistical estimation based on great amount of samples, draw the expression formula of damage probability.