CN103344448A - Method and system for identifying damage of bridge structure - Google Patents

Abstract

The invention discloses a method and system for identifying damage of a bridge structure. The method comprises the steps of arranging sensors on a target bridge, collecting pulse signals, collecting pulse signals of the target bridge structure under natural excitement with the sensors, obtaining high-precision impulse signals, acquiring incomplete modal parameters, conducting modal identification on the high-precision pulse signals through an improved NExT-ERA method, acquiring high-precision incomplete modal parameters, identifying the damage and establishing change rate indexes and indexes of incomplete modal strain energy, wherein the change rate indexes of the incomplete modal strain energy are used for representing damage positions, and the indexes of the incomplete modal strain energy are used for representing damage degrees. With the method for identifying the damage of the bridge structure, the damage positions and damage degrees of the target bridge structure can be obtained accurately, therefore, sudden disasters are prevented effectively, defect development is controlled timely, losses are cut, casualties are avoided, and the safety of the structure and users is guaranteed.

Description

Bridge structure damage identification method and system

Technical Field

The invention relates to the technical field of bridge structure damage identification, in particular to a bridge structure damage identification method and system based on pulse reaction at a limited measuring point.

Background

In recent years, bridge collapse accidents frequently occur, serious economic loss and social adverse effects are caused, and the safety problem of a bridge structure is widely concerned. Among many infrastructures, bridge structures play an extremely important role in national economy. Especially, the super-large bridge has high construction cost and large traffic flow, and is an important traffic hub for maintaining economic operation between areas and cities. The design life of the large-span bridge is dozens of years and hundreds of years, and the coupling effect of adverse factors such as long-term environmental corrosion, material aging, long-term effect of load, fatigue and mutation effect inevitably leads to damage accumulation and resistance attenuation of the structure, so that the capability of resisting natural disasters and even normal load is reduced, and catastrophic emergencies are caused under extreme conditions. The bridge operation condition is monitored in real time, so that sudden disasters can be effectively prevented, the development of defects can be controlled in time, the loss is reduced, casualties are avoided, and the safety of a structure and a user is ensured.

The existing and newly-built large-span bridges in China currently are generally provided with a structure real-time health monitoring system, and real-time early warning signals are provided by observing abnormal conditions of load and response in the operation process of the bridges, so that the safety of the structure and the operation is ensured; possible accumulated damage in the structure is discovered and identified as early as possible, and the damage condition is determined by auxiliary manual inspection; real-time security assessment is provided immediately after major disasters and emergencies. The most basic and key technology of the bridge health monitoring system is to extract useful structural characteristic information from the collected data, and accordingly find, locate and evaluate the damage condition of the structure, namely the damage identification of the structure. The current damage identification method has the following problems:

firstly, because the influence on traffic is caused, the artificial static and dynamic loading test of the large bridge is difficult, and the real-time monitoring is impossible, so that a natural excitation measuring mode is usually adopted at present. Natural excitation has many disadvantages; for example, the excitation is weak, the response is small, and the signal-to-noise ratio is low; for example, the bandwidth is narrow, and some modes cannot be excited; or only the output can be measured, and the input cannot be measured; and only modal frequency, mode shape and damping ratio can be obtained, and parameters such as modal stiffness, mass and the like cannot be obtained. Due to the defects, the precision of modal parameters obtained when the damage identification is carried out on the bridge structure is low, the error is large, and the final damage identification result is inaccurate.

Second, the response of a bridge structure to damage is generally small, and the sensitivity of the structural response is low. In many cases, the damage may be only a local phenomenon, and the local damage may not significantly affect the overall rigidity of the structure, but may be weaker in relation to the load-bearing capacity, so that the modal parameters obtained on the basis of the local damage may also have low precision and large error. In addition, for stiffening beams with complex shapes, different damages cause different changes of different elements of the stiffness matrix, and the obtained modal parameter error is too large.

Thirdly, the number of sensors installed on the large-span bridge is limited due to the reasons of operability, economy and the like, and in order to obtain as many structural damage information as possible through the limited number of sensors, the method can be realized by optimally arranging the limited number of sensors; however, current damage detection methods do not allow for optimal placement of sensors.

Disclosure of Invention

The invention aims to provide a method and a system for identifying damage of a bridge structure, which convert a high-precision pulse signal of the structure under natural excitation into a high-precision incomplete modal parameter through a modal identification method, and then carry out damage identification on the high-precision incomplete modal parameter, thereby accurately obtaining the damage position and the damage degree of a target bridge structure.

In order to achieve the above object, the present invention provides a method for identifying damage to a bridge structure, comprising:

arranging a sensor on the target bridge; acquiring a pulse signal of the target bridge structure under natural excitation through the sensor; acquiring a high-precision pulse signal;

carrying out modal identification on the high-precision pulse signal by an improved NExT-ERA method to obtain incomplete modal parameters; the improved NExT-ERA method adopts a 1-order Hankel matrix, and only uses singular vectors of the Hankel matrix but not singular values;

acquiring high-precision incomplete modal parameters; and carrying out damage identification on the high-precision incomplete modal parameters so as to obtain the damage position and the damage degree of the target bridge structure.

Optionally, the sensor is an acceleration sensor, and the acquired pulse signal is an acceleration signal.

Alternatively, the step of acquiring a high-precision pulsation signal may include filtering the pulsation signal by a low-pass filter.

Optionally, the low pass filter is a Chebyshev low pass filter.

Optionally, the incomplete modal parameter acquiring step comprises:

a. firstly constructing a Hankel partitioning matrix H₁，H₁＝hk[h(t_m)](ii) a Wherein hk represents the formation of H₁Operator of the matrix, h (t)_m) Representing an impulse response function matrix;

b. correlation function matrix R of discrete structure acceleration reaction under excitation of white noise_aa(τ_n) Substitute for H₁H (t) in (1)_m) And establishing a 1-order Hankel partitioning matrix H:

H＝hk₁[R_aa(τ_n)];

wherein the matrix τ_n=(n-1)Δt，n=1,2,...，；

c. Performing singular value decomposition on the H in the step b to obtain an orthogonal singular vector matrix U, V and a diagonal singular value matrix S;

d. constructing a system matrix A through an orthogonal singular vector matrix U and a diagonal singular value matrix S;

e. decomposing the characteristic value of the system matrix A to obtain the r-order frequency omega, the damping ratio xi and the vibration type vector

Optionally, the step of acquiring the incomplete modal parameters with high precision may include processing the incomplete modal parameters by a stable graph method.

Optionally, the step of performing damage identification on the high-precision incomplete modal parameter includes:

a. processing the high-precision incomplete modal parameters by a static method and/or a dynamic method to obtain an expanded complete modal;

b. obtaining structural incomplete strain energy according to the extended complete mode;

c. and respectively constructing an incomplete modal strain energy change rate index for representing the damage position and an incomplete modal strain energy index for representing the damage degree according to the incomplete strain energy.

Optionally, the method may further comprise a sensor arrangement optimization step comprising:

a. constructing a fitness function based on the incomplete modal strain energy index:

b. and optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm based on the fitness function.

Optionally, the method may further comprise a sensor arrangement optimization step comprising:

a. based on a finite n_mLimited N at one measuring point_mConstructing an incomplete modal compliance matrix difference by using the order incomplete modal parameters;

b. constructing an incomplete modal compliance difference damage index on the measured i-degree of freedom based on the incomplete modal compliance matrix difference;

c. constructing a fitness function based on an incomplete modal compliance difference damage index;

d. and optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm based on the fitness function.

The invention also discloses a bridge structure damage identification system, which comprises:

the sensor is arranged on a target bridge and used for collecting a pulse signal of the target bridge structure under natural excitation;

the signal processing unit is used for processing the pulse signal to obtain a high-precision pulse signal;

the mode identification unit is used for carrying out mode identification on the high-precision pulse signal through an improved NExT-ERA method so as to obtain incomplete mode parameters; the improved NExT-ERA method adopts a 1-order Hankel matrix, and only uses singular vectors of the Hankel matrix but not singular values;

the parameter processing unit is used for processing the incomplete modal parameters to obtain high-precision incomplete modal parameters;

and the damage identification unit is used for carrying out damage identification on the high-precision incomplete modal parameters so as to obtain the damage position and the damage degree of the target bridge structure.

Optionally, the system further comprises:

and the sensor arrangement optimization unit is used for optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm according to the relevant fitness function.

Optionally, the relevant fitness function is constructed by an incomplete modal strain energy indicator obtained in the damage identification unit.

Optionally, the constructing of the relevant fitness function includes:

a. based on a finite n_mLimited N at one measuring point_mConstructing an incomplete modal compliance matrix difference by using the order incomplete modal parameters;

b. constructing an incomplete modal compliance difference damage index on the measured i-degree of freedom based on the incomplete modal compliance matrix difference;

c. and constructing a fitness function based on the incomplete modal compliance difference damage index.

The invention has at least the following beneficial technical effects:

1) the invention can remove noise and other interference signals in the pulse signal under natural excitation, improve the precision of the pulse signal, and can improve the precision processing of the incomplete modal parameters obtained in the improved NExT-ERA method, so that the incomplete modal parameters with relatively high precision are obtained for damage identification, and the identification result is more accurate, thereby effectively preventing sudden disasters, controlling the development of defects in time, reducing loss, avoiding casualties and ensuring the safety of the structure and users;

2) the improved NExT-ERA method adopts a 1-order H matrix instead of a 0-order H matrix to solve modal parameters, does not use the singular value of a Hankel matrix, and only uses the singular vector to identify the modal parameters, thereby fully reducing modal identification errors and improving modal identification precision;

3) the pulse signals collected by the invention are acceleration signals, and the acceleration signals are collected by an acceleration sensor in the real-time health monitoring system of the structure, so that the collection is convenient and the cost is saved;

4) the high-frequency noise data in the acceleration signal can be filtered through low-pass filtering, so that the signal-to-noise ratio of the acceleration data is improved; furthermore, acceleration data obtained on each point distribution scheme is filtered by a Chebyshev low-pass filter, so that the filtering effect is better, modal identification can be concentrated on an interested frequency band to obtain a useful frequency band, and the modal identification precision is improved;

5) the invention can more simply carry out order determination on the characteristic system of the pulse signal by adopting a stable graph method, and the identification of true and false modes is easier;

6) according to the method, the damage index maximization is taken as a target, the arrangement of the sensors is optimized through a multi-population genetic algorithm, and particularly when the number of the sensors is limited, the limited number of the sensors can be configured at the optimal positions so as to obtain a relatively accurate pulse signal; in addition, the multi-population genetic algorithm can be adopted based on at least two fitness functions, so that the applicability is stronger.

Drawings

FIG. 1 is a schematic diagram of a full-bridge finite element model of a target bridge according to embodiment 1 of the present invention;

fig. 2 is a schematic view of an acceleration signal acquired in embodiment 1 of the present invention;

FIG. 3 is a schematic diagram of the acceleration signal after being processed by the filtering wave in embodiment 1 of the present invention

Fig. 4 is a flowchart of a method for identifying damage to a bridge structure in embodiment 1 of the present invention;

FIG. 5 is a flowchart of a method for identifying damage to a bridge structure according to another embodiment of the present invention;

FIG. 6 is a flowchart of the modality identification by the modified NExT-ERA method in example 1 of the present invention;

fig. 7 is a flowchart of performing damage identification on an incomplete modal parameter in embodiment 1 of the present invention;

fig. 8 is a flowchart of optimizing the sensor arrangement in embodiment 1 of the present invention;

FIG. 9 is a flow chart of optimizing sensor placement in other embodiments of the present invention;

fig. 10 is a schematic structural diagram of a system for identifying damage to a bridge structure in embodiment 2 of the present invention;

FIG. 11 is a schematic structural diagram of a damage identification system for a bridge structure according to another embodiment of the present invention;

the system comprises a sensor 1, a signal processing unit 2, a modal identification unit 3, a parameter processing unit 4, a damage identification unit 5 and a sensor arrangement optimization unit 6.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the following detailed description of the embodiments is provided with reference to the accompanying drawings.

According to the embodiment 1 of the invention, a bridge structure damage identification method is provided.

The total length of the target bridge is 5452m, the main bridge is a two-span continuous suspension bridge, the main span is 1650m, the side span is 578m, and the suspension bridge cable tower adopts a reinforced concrete door type frame structure consisting of tower columns and cross beams.

Firstly, establishing a finite element model, adopting a structural scheme of a three-dimensional beam-rod unit system and a stiffening beam 'fishbone beam', and establishing a pure rod system model by using ANSYS software. Since the bridge includes a plurality of components and has a complex structure, different components, such as sensors, may be arranged differently, and the measured structure may also be different, the present embodiment is mainly described with respect to the stiffening beam of the target bridge as a target. Fig. 1 shows a full-bridge finite element model, where N =3686 degrees of freedom are shared, the stiffening beam of the target bridge has 119 elements and 120 nodes, the numbering of the elements and nodes is l =1,2, …,119 and i =1,2, …,120, respectively, in the order from left to right in fig. 1, where node No. 30 corresponds to the north tower centerline of the target bridge. The booms of the target bridge are also numbered sequentially from left to right, and 119 × 2=238 booms. And marking a three-dimensional coordinate system where the structure is located as an x direction along the bridge direction, marking the vertical direction as a y direction, and marking the transverse bridge direction as a z direction.

As shown in the flowchart of fig. 4 of the method for identifying damage to a bridge structure of the present invention, the method for identifying damage to a bridge structure of the present embodiment may at least include steps 101 to 106 with respect to the target bridge.

Step 101, arranging sensors on a target bridge at equal intervals according to the vibration characteristics of the bridge structure. In this embodiment, 20 sensors are used, with 20 equally spaced points, and 1 point is selected every 6 points from the stiffening beam 3 rd node. In addition, the arrangement direction of the sensors on the stiffening beam is various, such as along the transverse bridge direction or along the vertical direction.

Step 102, collecting a pulsation signal of the target bridge structure under natural excitation. The pulsation signal may be acceleration data, and may be correspondingly acquired by using an acceleration sensor, and specifically, reference may be made to accelerator data acquired at one of the measurement points as shown in fig. 2. Under the general condition, the acceleration sensor in the real-time health monitoring system of bridge self structure is from the area, so can directly utilize and go on for gather convenient while practicing thrift the cost again. In other alternative embodiments, other data may also be used as the pulse signal, such as the displacement of the structure, and the corresponding sensor also uses a displacement sensor, which is not described in detail in this embodiment.

And 103, processing the pulse signal to obtain a high-precision pulse signal. In step 102, the acceleration sensor often has complex components in the acquired acceleration data, and the signal is also interfered by various noises during measurement, so that the acceleration sensor needs to process the signals, the signal-to-noise ratio of the acceleration data is improved, and a high-precision pulse signal is obtained. Finally, the high-precision acceleration data shown in fig. 3 can be obtained.

In this embodiment, acceleration data obtained on each point distribution scheme is filtered by a Chebyshev low-pass filter, so that modal identification can be concentrated on an interested frequency band to obtain a useful frequency band, and the modal identification precision is improved. Specifically, the low pass filtering of the acceleration data is processed in MATLAB using a function fitrpm comprising a Chebyshev low pass filter design to first determine the pass-stop band frequencies ω p, ω s and the pass-stop band frequenciesAnd (4) with ripples deltap and deltas, calculating the required filter order Ng by using a function firpmord, taking the Ng as an even number, and calculating the filter coefficient by using a function firrpm, thereby realizing the low-pass filtering of the acceleration data. In this embodiment, the passband frequency ω can be obtained_p16.7rad/s, stop band frequency ω_s18.8rad/s, passband ripple δ_p0.0005dB stop band ripple delta_s＝-35dB。

In other alternative embodiments, other types of low pass filters may be used to filter the acceleration data. However, the Chebyshev low-pass filtering method has better effect and higher precision, and the filtering effect is better than that of a window function-based digital filter.

And 104, performing modality recognition. The method comprises the steps of firstly improving an NExT-ERA method, and carrying out mode identification on the high-precision pulse signal through the improved NExT-ERA method to obtain incomplete mode parameters, so that mode identification errors are reduced, and mode identification precision is improved. Specifically, as shown in fig. 6, the modified NExT-ERA process may include steps 401 through 405.

Step 401, firstly constructing a Hankel partitioning matrix H₁，H₁＝hk[h(t_m)]；

Wherein hk represents the formation of H₁An operator of the matrix; h (t)_m) An impulse response function matrix; t is t_m= (m-1) Δ t is the point in time of discrete sampling; m =1,2, …, which is the number of displacement sampling points; Δ t is the sampling time interval.

Step 402, using a correlation function matrix R of discrete structure acceleration reaction under white noise excitation_aa(τ_n) Substitute for H₁H (t) in (1)_m) And establishing a 1-order Hankel block matrix H instead of the 0-order Hankel block matrix H, wherein the adoption of the 1-order Hankel matrix in the NExT-ERA method is the first point improvement of the NExT-ERA method, and the method is finally obtained:

H＝hk₁[R_aa(τ_n)];

wherein the matrix τ_n=(n-1)Δt，n=1,2,...，；

In addition, in other alternative embodiments, the correlation function matrix R of the displacement reaction can also be used_yy(τ_n) Substitute for H₁H (t) in (1)_m) And establishing a 1-order Hankel partitioning matrix H:

H＝hk₁[R_yy(τ_n)];

wherein the matrix R of the correlation function is a displacement response_yy(τ_n) The following method can be used to obtain the following:

firstly, the structure is n_fStructure pure pulse displacement response y (t) under dimensional pulse excitation f (t)_m)，

$y\left(t_m\right)={\∫}_{-\∞}^{\∞}h\left(\mathrm{\ρ}\right)f(t_m-\mathrm{\ρ})\mathrm{d\ρ};$

The displacement sampling points m =1,2, …, L =1+ T/Δ T, T is the time length, and Δ T is the sampling time interval; t <0 should be h (t) =0 and f (t) = 0.

Configuration y (t)_m) The autocorrelation function matrix is R_yy(τ_n)，

$R_{\mathrm{yy}}\left({\mathrm{\&tau;}}_n\right)=\frac{1}{L}\underset{m=1}{\overset{L}{\mathrm{\&Sigma;}}}y\left(t_m\right)y^T(t_m+{\mathrm{\&tau;}}_n)={\&Integral;}_{-\&infin;}^{\&infin;}{\&Integral;}_{-\&infin;}^{\&infin;}h\left(\mathrm{\&rho;}\right){\mathrm{\&Delta;}}_f({\mathrm{\&tau;}}_n+\mathrm{\&rho;}-\mathrm{\&upsi;})h^T\left(\mathrm{\&upsi;}\right)\mathrm{d\&rho;d\&upsi;};$

Wherein the correlation function samples τ_n=(n-1)Δt，n=1,2,...；Δ_fIs a cross-correlation matrix of the excitations,

${\mathrm{\&Delta;}}_f({\mathrm{\&tau;}}_n+\mathrm{\&rho;}-\mathrm{\&upsi;})=\underset{L\&RightArrow;\&infin;}{\lim }\frac{1}{L}\underset{m=1}{\overset{L}{\mathrm{\&Sigma;}}}f(t_m-\mathrm{\&rho;})f^T(t_m+{\mathrm{\&tau;}}_n-\mathrm{\&upsi;}).$

correlation function matrix R for acceleration response in this embodiment_aa(τ_n) Calculating method and correlation function matrix R of the displacement reaction_yy(τ_n) The calculation methods are the same, and the displacement correlation quantity in the above formulas can be obtained only by converting the displacement correlation quantity into the acceleration correlation quantity, and the specific calculation process is not repeated.

Step 403, performing Singular Value Decomposition (SVD) on H in step 402 to obtain H ═ USV^TAn orthogonal singular vector matrix U, V and a diagonal singular value matrix S are obtained.

Step 404, constructing a system matrix a and an observation matrix C by the orthogonal singular vector matrix U and the diagonal singular value matrix S, and embodying the second point improvement of the NExT-ERA method in the present invention, that is, only using singular vectors of the Hankel matrix but not using singular values thereof, to finally obtain:

A＝U_o(1:αn_m-n_m,:)⁺U_o(1+n_m:αn_m,:);

C＝U_o(1:n_m,:);

wherein n is_mFor measuring degrees of freedom, U_o=US^1/2The cross in the system matrix A is labeled to represent the Moore-Penrose inverse matrix.

Step 405, performing eigenvalue decomposition (EVD) on the system matrix a to obtain an eigenvector matrix Ψ and an eigenvalue matrix Λ', wherein the r-th order eigenvalue is μ_rThe characteristic vector is C psi_rObtaining the r order frequency omega, damping ratio xi and vibration mode vector of the structureRespectively, are as follows,

ω_r=|lnμ_r|/Δt,ξ_r=-ln|μ_r|/(ω_rΔt),

wherein, the r order frequency omega, the damping ratio xi and the vibration mode vector

Namely the incomplete modal parameters.

And 105, processing the incomplete modal parameters to obtain high-precision incomplete modal parameters. When SVD is performed on H in step 402, the number of non-zero singular values is larger than the order of the system due to noise, so that the order of the system is difficult to determine, and the identified modes often include noise modes and have low accuracy. Therefore, it is necessary to improve the accuracy, and the method used in this embodiment may be a stable graph method, which helps the system to determine the order and identify the true and false modes. Wherein, the stable graph method is 2 groups of r order modes which are identified when the order of the system is p +2 and pCompared with the state parameters (frequency, damping ratio and mode shape), p is generally an even number, and if the difference is smaller than a certain limit value, the r-order mode is called to be stable to p. At omega_rAnd establishing a rectangular coordinate system by taking the abscissa as the abscissa and the ordinate as the p, marking the condition that the r-order mode is stable to the p in the coordinate system by using a certain pattern to form a stable graph, wherein the stable coordinate points marked as stable points are called stable points, and an axis formed by the stable points of the same-order mode is called a stable axis. If ω, ξ and the mode vectorMAC value of

The limit values are respectively expressed as epsilon_ω、ε_ξAnd

the condition that the nth order modal frequency omega and the damping ratio xi are stable to p is as follows:

$\left|\frac{{\mathrm{\&omega;}}_{p,r}-{\mathrm{\&omega;}}_{p+2,r}}{{\mathrm{\&omega;}}_{p,r}}\right|\&le;{\mathrm{\&epsiv;}}_{\mathrm{\&omega;}},$

$\left|\frac{{\mathrm{\&xi;}}_{p,r}-{\mathrm{\&xi;}}_{p+2,r}}{{\mathrm{\&xi;}}_{p,r}}\right|\&le;{\mathrm{\&epsiv;}}_{\mathrm{\&xi;}};$

in the formula of omega_p,rAnd xi_p,rThe r order circle frequency and the damping ratio obtained when p is taken for the order of the system respectively; similarly, r order mode vector can be obtained

The conditions for p stabilization were:

in the formula

And the r order vibration mode vector is obtained when the order of the system is p.

And 106, performing a damage identification process on the high-precision incomplete modal parameters to obtain a damage position parameter and a damage degree parameter of the target bridge structure. The step of identifying the damage in this embodiment may specifically include steps 501 to 503 shown in fig. 7.

In step 501, the high-precision incomplete modal parameters obtained in the stable graph method are processed by a static method and/or a dynamic method, that is, the static method and the dynamic method can be simultaneously processed, or only one of the static method and the dynamic method is used for processing, so that an expanded complete modal is obtained; it should be noted that there is no sequence in the simultaneous static and dynamic processes.

In the case of the static method, the imperfect mode of vibration in the imperfect parameters obtained in step 105 is extended to a full degree of freedom. Then, the displacement vector u of the complete freedom degree is distinguished into the component u of the main freedom degree_mAnd component u of the secondary degree of freedom_sThus forming a characteristic equation in block form:

$\left[\begin{array}{cc}{M}_{\mathrm{mm}}& M_{\mathrm{ms}}\\ M_{\mathrm{sm}}& M_{\mathrm{ss}}\end{array}\right]\left\{\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_m\\ {\stackrel{\&CenterDot;\&CenterDot;}{u}}_s\end{array}\right\}+\left[\begin{array}{cc}{K}_{\mathrm{mm}}& K_{\mathrm{ms}}\\ K_{\mathrm{sm}}& K_{\mathrm{ss}}\end{array}\right]\left\{\begin{array}{c}{u}_m\\ u_s\end{array}\right\}=\left\{\begin{array}{c}{f}_m\\ f_s\end{array}\right\};$

wherein M is a block structure mass matrix in a kinetic formula,

the present embodiment is considered to omit the influence of the inertial force and the load vector of the secondary degree of freedom, i.e., the inertial force and the f load vector

f_s=0, thereby obtaining a transformation matrix T_G：

$\left\{\begin{array}{c}{u}_m\\ u_s\end{array}\right\}=\left[\begin{array}{c}I\\ {{-K}_{\mathrm{ss}}}^{-1}{K}_{\mathrm{sm}}\end{array}\right]u_m=T_G{u}_m;$

Wherein K is a block structure rigidity matrix in a dynamic formula, and I represents an identity matrix.

The resulting extended (denoted by subscript E) complete modality is:

wherein

The obtained r-th order incomplete mode at the incomplete measuring point.

For the dynamic method, the acceleration vector is taken as a certain specific circular frequency omega₀The component (c):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_m\\ {\stackrel{\&CenterDot;\&CenterDot;}{u}}_s\end{array}\right\}={-\mathrm{\&omega;}}_0^2\left\{\begin{array}{c}{u}_m\\ u_s\end{array}\right\};$

neglecting the effect of the load vector of the secondary degree of freedom, i.e. f_s=0, thereby obtaining a transformation matrix T_D：

$\left\{\begin{array}{c}{u}_m\\ u_s\end{array}\right\}=\left[\begin{array}{c}I\\ -{(K_{\mathrm{ss}}-{\mathrm{\&omega;}}_0^2{M}_{\mathrm{ss}})}^{-1}(K_{\mathrm{sm}}-{\mathrm{\&omega;}}_0^2{M}_{\mathrm{sm}})\end{array}\right]u_m=T_D\left({\mathrm{\&omega;}}_0\right)u_m;$

The resulting extended (denoted by subscript E) complete modality is:

wherein

The obtained r-th order incomplete mode at the incomplete measuring point.

And 502, obtaining structural incomplete strain energy according to the extended complete mode. In particular according to the static or dynamic method

Further, the incomplete strain energy of the whole structure and the l unit under the expansion mode of the r order is determined by the following formula:

where K represents the stiffness matrix of the structure.

And 503, respectively constructing an incomplete modal strain energy change rate index for representing the damage position and an incomplete modal strain energy index for representing the damage degree according to the incomplete strain energy.

The incomplete modal strain energy change rate index representing the damage position is as follows:

${\mathrm{MSECR}}_{l,E}=\frac{1}{N_m}\underset{r=1}{\overset{N_m}{\mathrm{\&Sigma;}}}{\mathrm{MSECR}}_{\mathrm{lr},E}=\frac{1}{N_m}\underset{r=1}{\overset{N_m}{\mathrm{\&Sigma;}}}\frac{P_{\mathrm{lr},E}^d-P_{\mathrm{lr},E}^u}{P_{r,E}^u};$

wherein N is_mIs the modal total order used for lesion identification.

The incomplete modal strain energy index representing the damage degree is:

${\mathrm{\&alpha;}}_{l,E}^a=1-\frac{1}{N_m}\sqrt{\frac{P_{\mathrm{lr},E}^u}{P_{\mathrm{lr},E}^d}},l=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_e,0\&le;{\mathrm{\&alpha;}}_{l,E}^a<1;$

and 107, judging the damage position of the structure according to the incomplete modal strain energy change rate index parameter, and judging the damage degree of the structure according to the incomplete modal strain energy index parameter. In this embodiment, particularly for the case that the stiffening beam is in the horizontal and vertical directions of the bridge, the finally obtained results of determining the structural damage position and determining the structural damage degree can refer to the following table:

wherein, the damage position can be judged according to the damage unit number l and the damage degree alpha_lAnd judging the damage degree.

According to the invention, interference signals such as noise in the pulse signal under natural excitation can be removed, and the high-precision pulse signal can be obtained, so that incomplete modal parameters with relatively high precision can be obtained; in addition, the accuracy of the incomplete modal parameters is improved before the structural damage identification is carried out, the accuracy of the structural damage identification result is further improved, sudden disasters can be effectively prevented through the damage identification result, the development of defects can be controlled in time, the loss is reduced, the casualties are avoided, and the safety of the structure and a user is ensured.

Of course, in this embodiment, the step 106 and the step 107 may be combined into one step, that is, the damage position parameter and the damage degree parameter of the target bridge structure are obtained, so as to obtain the damage position and the damage degree of the target bridge structure.

As particularly shown in fig. 5, in other alternative embodiments, the method of the present invention may further include step 108. Step 108 is to optimize the sensor arrangement by multi-population genetic algorithm with the goal of maximizing the damage index. Particularly, sensors cannot be arranged in all degrees of freedom of a health monitoring system of a large bridge structure, so that the arrangement of a limited number of sensors can be optimized, a better monitoring effect can be achieved, and as much structural damage information as possible can be obtained. The step of optimizing the arrangement of the sensors by the multi-population genetic algorithm in the present embodiment may specifically include steps 801 to 802 as shown in fig. 8.

Step 801, constructing a fitness function based on the incomplete modal strain energy index. In particular, the amount of the solvent to be used,

for incomplete modal strain energy indexes, the constructed fitness function is as follows:

$f_{\mathrm{MSE}}=\underset{l=1}{\overset{n_{\mathrm{be}}}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{l,E}^a;$

wherein, let f_MSEMaximum point placement scheme corresponds to

The damage recognition ability of the index is strongest, n_beAnd the degree of freedom of the imperfect vibration mode is shown.

And 802, optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm based on the fitness function. Specifically, in the process of performing optimal sensor layout by using the multi-population genetic algorithm, the evolutionary process and parameter setting may include the following steps:

1) and randomly generating 12 sub-populations with 30 individuals in each sub-population. The point distribution condition of the sensor on the degree of freedom is only divided into yes and no values, so that a binary mode is suitable to be adopted, and the length of the data string is 120 of the total number of the alternative measuring points.

2) Selecting individuals participating in evolution to pair the subgroups through selective operation; then, carrying out two-point cross operation on the paired individuals for three times by using the probability 1 to obtain six filial individuals, and selecting two optimal individuals from the parent individuals and the filial individuals as new-generation individuals according to the fitness value, namely two-eighths survival selection; and then carrying out variation operation of two-eighth survival selection on the filial generation, finally inserting the filial generation into the original population, eliminating bad individuals according to the fitness, and recording the individuals with the optimal fitness value in all the individuals after evolution.

3) And after every 10 generations in the step 2, carrying out individual migration operation among the sub-populations, wherein the migration probability is 0.30.

4) The whole process is divided into two stages of gradual change and abrupt change. The initial progression is a gradual change stage, mainly by cross operation, and the variation rate is 0.01. When the optimal value of global individual fitness is continuously stable and unchanged for 15 generations, a sudden change stage is entered, the stage takes variation as main operation, and the variation rate is 0.12. It is noted that the algorithm is sensitive to variations of both of the variation parameters.

5) Comparing the individuals with the optimal fitness value obtained in each evolution process, stopping evolution when the difference between the optimal fitness values of continuous 25 generations is within ten thousandth, and giving the optimal fitness value; otherwise, the evolution continues until a set maximum allowed evolution algebra 240.

In addition, in other alternative embodiments of the present invention, other indicators than the incomplete modal strain energy indicator may also be used to construct the fitness function in step 801 included in step 108 described above. For example, a fitness function may be constructed by using an incomplete modal compliance difference damage index, and then the sensor arrangement may be optimized by using a multi-population genetic algorithm based on the fitness function, which may specifically include steps 901 to 904 shown in fig. 9.

Step 901, define n based on finite_mLimited N at one measuring point_mImperfect modal compliance matrix difference of order imperfect modal parameters:

wherein,

for an imperfect modal compliance matrix after damage,

is an incomplete modal compliance matrix before damage;

step 902, defining an incomplete modal compliance difference damage index on the measured i-degree of freedom as:

flex_itr≡max|ΔF_tr(:,i)|,i＝1,2,…,n_m

step 903, according to incomplete mode softnessDegree difference damage index flex_itrThe fitness function is constructed as follows:

$f_{\mathrm{FLEX}}=\underset{i=1}{\overset{n_m}{\mathrm{\&Sigma;}}}{\mathrm{flex}}_{i,\mathrm{tr}};$

wherein, let f_FLEXFlex corresponding to maximum stationing scheme_itrThe damage identification capability of the index is strongest.

And 904, optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm based on the fitness function.

Step 901 to step 903 in the present embodiment may replace step 801 in the above embodiment, and step 904 is equivalent to step 802 in the above embodiment. The evolution process and the setting of parameters in the multi-population genetic algorithm of the present embodiment are the same as those in the above embodiments, and are not described in detail.

Embodiment 2 of the present invention further provides a system for identifying damage to a bridge structure, as shown in fig. 10, which may include:

the sensor 1 is arranged on a target bridge and used for collecting a pulse signal of a target bridge structure under natural excitation; the sensor 1 in this embodiment may be an acceleration sensor, and the corresponding pulsation signal is an acceleration signal.

The signal processing unit 2 is used for processing the pulse signal to obtain a high-precision pulse signal; the signal processing module in this embodiment may include MATLAB software, a Chebyshev low-pass filter, and the like, and the Chebyshev low-pass filter is used to perform low-pass filtering processing on the pulsation signal, where the filtering process of the signal is performed in the MATLAB software. It should be noted that, in other alternative embodiments, the above processing may not be performed on the pulse signal, but the pulse signal is directly transmitted to the following mode identification unit 3 for mode identification, but the finally obtained mode identification result is not as accurate as the result obtained after the processing by the signal processing unit 2 in this embodiment.

The mode identification unit 3 is used for carrying out mode identification on the high-precision pulse signal through an improved NExT-ERA method so as to obtain incomplete mode parameters; wherein, the improved NExT-ERA method adopts a Hankel matrix of 1 order, and only uses singular vectors of the Hankel matrix and does not use singular values thereof.

The parameter processing unit 4 is configured to process the incomplete modal parameter to obtain a high-precision incomplete modal parameter; in this embodiment, the incomplete modal parameters are mainly processed by a stable graph method.

And the damage identification unit 5 is used for carrying out damage identification on the high-precision incomplete modal parameters so as to obtain the damage position and the damage degree of the target bridge structure, so that sudden disasters can be effectively prevented, the development of defects can be controlled in time, the loss is reduced, the casualties are avoided, and the safety of the structure and a user is ensured.

In addition, as shown in fig. 11, in other alternative embodiments, the bridge structure damage identification system of the present invention may further include a sensor arrangement optimization unit 6 that optimizes the arrangement of the sensors based on the corresponding fitness function using a multi-population genetic algorithm. However, when the fitness function is specifically selected, the following two schemes are possible, as in the embodiment of the method of the present invention.

The first method is to construct a fitness function through the incomplete modal strain energy index obtained in the damage identification unit 5, so that the arrangement of the sensors is optimized through the fitness function by adopting a multi-population genetic algorithm.

Another by a finite n_mLimited N at one measuring point_mAnd constructing an incomplete modal compliance matrix difference by using the order incomplete modal parameters, constructing an incomplete modal compliance difference damage index on the measured i-degree of freedom by using the incomplete modal compliance matrix difference, constructing a fitness function by using the incomplete modal compliance difference damage index, and finally optimizing the arrangement of the sensors by using a multi-population genetic algorithm according to the fitness function.

The two schemes can optimize the arrangement of the sensors, and particularly, the sensors cannot be arranged in all degrees of freedom of a health monitoring system of a large bridge structure, so that the arrangement of a limited number of sensors can be optimized, a better monitoring effect can be achieved, and as much structural damage information as possible can be obtained.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (13)

1. A bridge structure damage identification method is characterized by comprising the following steps:

arranging a sensor on the target bridge;

acquiring a pulse signal of the target bridge structure under natural excitation through the sensor;

acquiring a high-precision pulse signal;

carrying out modal identification on the high-precision pulse signal by an improved NExT-ERA method to obtain incomplete modal parameters; the improved NExT-ERA method adopts a 1-order Hankel matrix, and only uses singular vectors of the Hankel matrix but not singular values;

acquiring high-precision incomplete modal parameters;

and carrying out damage identification on the high-precision incomplete modal parameters so as to obtain the damage position and the damage degree of the target bridge structure.

2. The bridge structure damage identification method according to claim 1, wherein the sensor is an acceleration sensor, and the collected pulsation signal is an acceleration signal.

3. The bridge structure damage identification method according to claim 1 or 2, wherein the step of acquiring a high-precision pulse signal comprises:

and filtering the pulsation signal through a low-pass filter.

4. The bridge structure damage identification method according to any one of claims 3, wherein the low pass filter is a Chebyshev low pass filter.

5. The bridge structure damage identification method according to any one of claims 1 to 4, wherein the incomplete modal parameter obtaining step comprises:

a. firstly constructing a Hankel partitioning matrix H₁，H₁＝hk[h(t_m)](ii) a Wherein hk represents the formation of H₁Operator of the matrix, h (t)_m) Representing an impulse response function matrix;

b. correlation function matrix R of discrete structure acceleration reaction under excitation of white noise_aa(τ_n) Substitute for H₁H (t) in (1)_m) And establishing a 1-order Hankel partitioning matrix H:

H＝hk₁[R_aa(τ_n)];

wherein the matrix τ_n=(n-1)Δt，n=1,2,...，；

c. Performing singular value decomposition on the H in the step b to obtain an orthogonal singular vector matrix U, V and a diagonal singular value matrix S;

d. constructing a system matrix A through an orthogonal singular vector matrix U and a diagonal singular value matrix S;

e. decomposing the characteristic value of the system matrix A to obtain the r-order frequency omega, the damping ratio xi and the vibration type vector

6. The bridge structure damage identification method according to claims 1-5, wherein the step of obtaining high-precision imperfect modal parameters comprises:

and processing the incomplete modal parameters by a stable graph method.

7. The bridge structure damage identification method according to claims 1-6, wherein the step of performing damage identification on the high-precision imperfect modal parameters comprises:

a. processing the high-precision incomplete modal parameters by a static method and/or a dynamic method to obtain an expanded complete modal;

b. obtaining structural incomplete strain energy according to the extended complete mode;

c. and respectively constructing an incomplete modal strain energy change rate index for representing the damage position and an incomplete modal strain energy index for representing the damage degree according to the incomplete strain energy.

8. The bridge structure damage identification method of claim 7, further comprising a sensor arrangement optimization step comprising:

a. constructing a fitness function based on the incomplete modal strain energy index:

b. and optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm based on the fitness function.

9. The bridge structure damage identification method of claim 7, further comprising a sensor arrangement optimization step comprising:

a. based on a finite n_mLimited N at one measuring point_mConstructing an incomplete modal compliance matrix difference by using the order incomplete modal parameters;

b. constructing an incomplete modal compliance difference damage index on the measured i-degree of freedom based on the incomplete modal compliance matrix difference;

c. constructing a fitness function based on an incomplete modal compliance difference damage index;

d. and optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm based on the fitness function.

10. A bridge structure damage identification system, comprising:

the sensor is arranged on a target bridge and used for collecting a pulse signal of the target bridge structure under natural excitation;

the signal processing unit is used for processing the pulse signal to obtain a high-precision pulse signal;

the mode identification unit is used for carrying out mode identification on the high-precision pulse signal through an improved NExT-ERA method so as to obtain incomplete mode parameters; the improved NExT-ERA method adopts a 1-order Hankel matrix, and only uses singular vectors of the Hankel matrix but not singular values;

the parameter processing unit is used for processing the incomplete modal parameters to obtain high-precision incomplete modal parameters;

and the damage identification unit is used for carrying out damage identification on the high-precision incomplete modal parameters so as to obtain the damage position and the damage degree of the target bridge structure.

11. The bridge structure damage identification system of claim 10, further comprising:

and the sensor arrangement optimization unit is used for optimizing the arrangement of the sensors by adopting a multi-population genetic algorithm according to the relevant fitness function.

12. The bridge structure damage identification system of claim 11, wherein the correlation fitness function is constructed from imperfect modal strain energy indicators obtained in the damage identification unit.

13. The bridge structure damage identification system of claim 11, wherein the constructing of the correlation fitness function comprises:

a. based on a finite n_mLimited N at one measuring point_mConstructing an incomplete modal compliance matrix difference by using the order incomplete modal parameters;

b. constructing an incomplete modal compliance difference damage index on the measured i-degree of freedom based on the incomplete modal compliance matrix difference;

c. and constructing a fitness function based on the incomplete modal compliance difference damage index.

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