CN114692465B - Nondestructive identification method, storage medium and equipment for bridge damage position - Google Patents

Nondestructive identification method, storage medium and equipment for bridge damage position Download PDF

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CN114692465B
CN114692465B CN202210398866.7A CN202210398866A CN114692465B CN 114692465 B CN114692465 B CN 114692465B CN 202210398866 A CN202210398866 A CN 202210398866A CN 114692465 B CN114692465 B CN 114692465B
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张延哲
丁勇
张立平
卜建清
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Harbin Institute of Technology
Shijiazhuang Tiedao University
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Abstract

A nondestructive identification method, storage medium and equipment for a bridge damage position belong to the technical field of bridge engineering health monitoring. In order to solve the problem that the existing detection technology cannot simply identify the damage position of the bridge structure, the invention determines the damage position based on the unscented Kalman filter algorithm and the self-adaptive unscented Kalman filter algorithm, calculates the corresponding sensitive parameter of each step in the filtering process, and calculates the corresponding sensitive parameter eta according to the sensitive parameter eta k Selecting the filter algorithm of the next time step, forming a new diagonal square matrix according to all main diagonal elements of state quantity covariance when executing the adaptive unscented Kalman filter algorithm, sequentially expanding the covariance value corresponding to each elastic modulus parameter of the square matrix, executing one-step complete unscented Kalman filter operation and obtaining a sensitivity parameter eta k And finding the damage position; expanding covariance corresponding to the position and continuing to execute the (k+1) th time step until all the cycles are finished to obtain all the damage positions.

Description

Nondestructive identification method, storage medium and equipment for bridge damage position
Technical field:
the invention belongs to the technical field of bridge engineering health monitoring, and particularly relates to a nondestructive identification method, a storage medium and equipment for a bridge damage position.
The background technology is as follows:
the bridge is used as a node and a throat in traffic and transportation life line engineering, and has irreplaceable effects in the aspects of promoting regional link, guaranteeing material transportation, promoting economic development and the like. With the increase of the service life of the bridge, the influence of heavy traffic effect, environmental erosion, material aging, fatigue effect and the like on the performance of the bridge structure is larger and larger, so that the local resistance of the bridge is reduced, the damage is accumulated, and the damage and even collapse are induced. How to acquire the damage position of the bridge as soon as possible is significant in the aspects of timely maintenance, wide-range damage prevention, personnel safety guarantee, energy conservation and environmental protection.
At present, according to whether an original structure is damaged or not, the bridge damage position detection method is mainly divided into two types, namely a damage detection method and a nondestructive detection method, wherein the damage detection method mainly comprises the steps of obtaining a physical sample of a certain position of a bridge by means of a tool, such as punching and sampling, and further observing or testing and analyzing, which can definitely influence the original structure, and has low detection speed and low efficiency; nondestructive testing methods include ultrasonic detection techniques, acoustic emission detection techniques, ground penetrating radar detection techniques, and the like, but all of which require specialized equipment, are relatively costly to detect, and require specialized technician operation. Therefore, there is a need to develop a nondestructive inspection method suitable for bridge structures and easy to operate.
The invention comprises the following steps:
the invention aims to solve the problem that the existing detection technology cannot simply identify the damaged position of a bridge structure, and further provides a nondestructive identification method for the damaged position of the bridge.
A nondestructive identification method for a damaged position of a bridge comprises the following steps:
for the bridge structure, determining initial values of corresponding states of the bridge structure, and forming initial state quantity χ 0 And determining covariance matrix of initial state quantity according to Kalman filtering principle, namely initial state quantity covariance P 0 The method comprises the steps of carrying out a first treatment on the surface of the Wherein χ is 0 And P 0 State quantity and state quantity covariance, respectively, referred to as time step 0;
based onThe unscented Kalman filter algorithm performs preliminary identification, and in the process of performing preliminary identification based on the unscented Kalman filter algorithm, the measurement update step based on the unscented Kalman filter algorithm is required to calculate the observation error epsilon of the kth time step k And a k-th time step of metrology prediction covariance P yy,k And based on epsilon k And P yy,k Calculating and outputting the corresponding sensitive parameters of each step
Then the output sensitivity parameter eta is plotted k If eta k If peak pulse appears in the time course curve, the damage position is identified based on the self-adaptive unscented Kalman filter algorithm, and in the process of identifying based on the self-adaptive unscented Kalman filter algorithm, the calculated eta is required to be judged k And sensitivity parameter threshold eta 0 If eta k ＜η 0 Continuing to identify based on the unscented Kalman filter algorithm; if eta k ≥η 0 The following steps are continued:
setting an initial value to 0 and dimension to be equal to initial state quantity χ 0 Is denoted by the letter L; taking state quantity covarianceAll major diagonal elements of (a) constitute a new diagonal matrix ++>The positions of the original diagonal elements are kept unchanged; sequentially enlarge->The corresponding covariance value of each elastic modulus parameter is expanded each time, one-step complete unscented Kalman filtering operation is carried out, and aiming at the expansion of the row number or the column number z corresponding to the covariance value, one-step complete unscented Kalman filtering operation is carried out to obtain a sensitivity parameter eta k Let L (z) =η k The method comprises the steps of carrying out a first treatment on the surface of the Finding the minimumPosition number z corresponding to L of (2) min This location is the lesion location; then let->Expanding 20 times, and continuing to execute the (k+1) th time step, and judging eta again k+1 And sensitivity parameter threshold eta 0 Until all cycles are completed to obtain all lesion locations.
Further, in the process of identifying by using the unscented Kalman filter algorithm and in the process of identifying by using the adaptive unscented Kalman filter algorithm, the vertical displacement response of each beam unit node is selected as an observation value y.
Further, the bridge structure corresponding state comprises the elastic modulus of each bridge unit, and the displacement and the speed of the bridge structure.
Further, in the process of identification based on the adaptive unscented Kalman filter algorithm, the sensitivity parameter eta is calculated k The process of (1) comprises the following steps:
step 7.1, based on the UT transformation principle of the unscented kalman filter algorithm, using the state quantity χ of the (k-1) th time step k-1 And state quantity covariance P k-1 Generating (2n+1) sigma points, and solving the state quantity corresponding to each sigma point through a state equationWherein k starts from 1 and k.epsilon.1, N]N is the total time step number, N is the dimension of the state quantity, i is the ith sigma point, and i E [1,2n+1 ]]；
Step 7.2, the time update step based on the unscented Kalman filter algorithm completes the update of the state quantity and the state quantity covariance from the (k-1) th time step to the kth time step, respectively written asAnd->The formula is as follows:
in the method, in the process of the invention,and->Weight values of the ith sigma point of the kth time step, respectively, +.>For the state quantity estimated value corresponding to the ith sigma point of the kth time step, Q k Noise for the kth time step;
step 7.3, using the UT transformation principle based on the unscented kalman filter algorithm, updated in step 7.2Andgenerating (2n+1) sigma points, and solving an observation estimated value corresponding to each sigma point through an observation equation>
Step 7.4, calculating and outputting the measurement predicted value of the kth time step based on the measurement update step of the unscented Kalman filter algorithmAnd->
In the middle of，Weight value for the ith sigma point of the kth time step,/for the kth time step>The observation estimated value corresponding to the ith sigma point in the kth time step is obtained;
step 7.5, calculating the observed error epsilon of the kth time step based on the measurement updating step of the unscented Kalman filter algorithm k And (2) and
wherein y is k As an observation of the kth time step,measuring a predicted value for the kth time step;
step 7.6, calculating the measurement prediction covariance P of the kth time step based on the measurement update step of the unscented Kalman filter algorithm yy,k And (2) and
in the method, in the process of the invention,weight value for the ith sigma point of the kth time step,/for the kth time step>For the observation estimate corresponding to the kth time step i sigma point,/for the k time step i sigma point>For the measurement prediction value of the kth time step, R k Noise for the kth time step;
step 7.7 epsilon calculated based on step 7.5 and step 7.6 k And P yy,k Construction sensitivity parameter eta k And (2) andand calculate and output eta for each step k Values.
Further, in the process of identification based on the adaptive unscented Kalman filter algorithm, the calculation sensitivity parameter eta is obtained k Then calculate the kth time stepAnd->Cross covariance P of (2) xy,k And updating data, wherein the specific process comprises the following steps:
step 7.8, calculating the kth time step based on the measurement update step of the unscented Kalman filter algorithmAnd->Cross covariance P of (2) xy,k ，/>
Step 7.9, updating the Kalman gain matrix of the kth time step:
step 7.10, updating and outputting the state quantity of the kth time step:
step 7.11, updating and outputting the state quantity covariance of the kth time step:
further, find the minimum L corresponding position number z min Is provided with (1)The body process comprises the following steps:
step 7.14, covariance the state quantity of the kth time stepMarking the row number or column number of the covariance value corresponding to the first elastic modulus parameter in the main diagonal element as m, and adding the state quantity covariance +.>The row number or column number of the covariance value corresponding to the last elastic modulus parameter in the main diagonal element is marked as l, and the total number of the elastic modulus parameters is (l-m+1);
taking the current time stepAll major diagonal elements of (a) constitute a new diagonal matrix ++>The positions of the original diagonal elements are kept unchanged; sequentially enlarge->The corresponding covariance value of each elastic modulus parameter of the rubber belt is thatAnd only one covariance value is enlarged at a time,/->The remaining element values of (2) remain unchanged, wherein +.>And->Respectively representing the coordinate variance values of the z position of the row number and the column number, and being a scalar; lambda is an expansion multiple;
z initiationThe value is m, and z is [ m, l-m+1 ]]The method comprises the steps of carrying out a first treatment on the surface of the Calculated from z=mAnd the state quantity of the kth time step +.>Executing one-step complete unscented Kalman filtering operation, namely executing the steps 7.1 to 7.11, and outputting eta k Let L (z) =η k ；
Step 7.15, let z=m+1, continue to execute step 7.14 until z=l-m+1 ends;
step 7.16, not counting zero value, finding the position number corresponding to the minimum value in L, and marking as z min Z, i.e. z min Is the location of the injury.
Further, the expansion factor λ=1×10 ω ，10 ω Equal to the initial state quantity covariance P 0 Reciprocal of the smallest order of magnitude in (c).
Further, a motion control differential equation or a finite element model corresponding to the bridge structure is built based on the Euler-Bernoulli beam units.
A storage medium having stored therein at least one instruction loaded and executed by a processor to implement the method of non-destructive identification of a bridge damage location.
A device for non-destructive identification of a damaged bridge location, the device comprising a processor and a memory, the memory having stored therein at least one instruction, the at least one instruction being loaded and executed by the processor to implement a method for non-destructive identification of a damaged bridge location.
The beneficial effects are that:
the method can identify the damage position of the bridge based on the local vertical displacement response of the bridge as an observation value, is simple to operate, and does not damage the original structure. Meanwhile, the method for identifying the damaged position of the bridge is beneficial to timely maintenance of the bridge structure, can effectively prevent large-area damage, and accords with the development concepts of environmental protection, energy conservation and low carbon.
Description of the drawings:
for ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.
FIG. 1 is a plot of sensitivity parameter time course.
FIG. 2 is a graph showing the effect of a peak pulse on a sensitivity parameter time course curve.
Fig. 3 is a partial view of fig. 2.
FIG. 4 is a diagram of a vehicle-bridge coupling system of an embodiment in which a vehicle travels from one end of a bridge to the other at a speed, in which the body mass of a 1-quarter vehicle model is represented by the letter m 1 A representation; suspension stiffness between the body and the tire of a 2-quarter vehicle model, denoted by the letter k 1 A representation; suspension damping between the body and the tire of a 3-quarter vehicle model, using the letter c 1 A representation; tire mass for 4-quarter vehicle model, denoted by the letter m 2 A representation; contact stiffness between a tire of a 5-quarter vehicle model and a bridge, using the letter k 2 A representation; 6-contact point of the tire and the bridge; 7-a fixed end of a simply supported boundary constraint; 8-beam units; 9-beam unit nodes; 10-simply supported boundary constrained slide end.
The specific embodiment is as follows:
for the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention is described below by means of specific embodiments shown in the accompanying drawings. It should be understood that the description is only illustrative and is not intended to limit the scope of the invention. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the present invention.
It should be noted here that, in order to avoid obscuring the present invention due to unnecessary details, only structures and/or processing steps closely related to the solution according to the present invention are shown in the drawings, while other details not greatly related to the present invention are omitted.
When the damage position is identified, the damage index is required to be formulated first, and whether the bridge structure is damaged or not is judged based on the damage index. The mass of the bridge structure is generally considered constant, damping is a function of mass and stiffness, and for ease of analysis, rayleigh damping is generally assumed, whereby bridge damage indicators are generally reflected by stiffness parameters. Further, stiffness consists of modulus of elasticity and moment of section inertia, and changes in bridge cross-section are generally ignored. Therefore, the index of damage of a deeper layer is represented by a microscopic parameter of elastic modulus. In addition, considering timeliness of damage position identification and dimensional characteristics of a bridge, a finite element model of the bridge is generally built based on Euler-Bernoulli beam units, or a motion control differential equation of a bridge structure is built based on the Euler-Bernoulli beam units; and this is taken as a reasonable simplification of the real bridge structure. The displacement, speed and other responses of the bridge structure can be represented by corresponding values of the degrees of freedom of the beam unit nodes, and the elastic modulus attribute of each beam unit can be independently endowed. Therefore, the specific damage position of the bridge can be judged according to the attribute of different beam units.
The first embodiment is as follows:
the embodiment is a nondestructive identification method for the damaged position of the bridge, and the method is based on the local vertical displacement response of the bridge, so the method is a nondestructive identification method for identifying the damaged position of the bridge based on the local vertical displacement response of the bridge, and is essentially an identification method based on a self-adaptive unscented Kalman filter algorithm.
The nondestructive identification method for the damaged position of the bridge comprises the following steps:
step 1, deducing a motion control differential equation of a structure or establishing a structure finite element model according to the Darby principle, the structure dynamics and the finite element theory, wherein the structure is a bridge structure, and is convenient to express and short for structure;
in the process, a motion control differential equation or a finite element model of the bridge structure is established based on Euler-Bernoulli beam units, and the elastic modulus of each beam unit is used as a damage index;
step 2, displacing the structure by X and the structure speedAndthe vector of elastic modulus E is called the state quantity, symbolized byA representation;
in some embodiments, according to the state quantity χ, the equation relationship for solving the state quantity is deduced according to the motion control differential equation of the structure in the step 1 and based on the linear algebraic matrix operation and numerical differential and integral operation of numerical analysis, or based on the linear algebraic matrix operation and numerical integral method such as Newmark- β method of structural dynamics;
or,
in other embodiments, according to the state quantity χ, performing output setting of the state quantity according to the finite element model of the structure in the step 1, and taking the state quantity χ as a state equation; the noise effect is considered in the process;
and 3, taking the vertical displacement response of each beam unit node acquired by the sensor as an observation value y.
The observed value generally means a series of physical quantities including displacement, velocity, acceleration, strain, stress, force, etc., which can be measured by a sensor, and in the bridge structure, a displacement measured value is used as the observed value in the present embodiment.
In the invention, the state equation is differential operation of state quantity, the state quantity is written in the form of displacement and speed, which is convenient for deducing the state equation, because the derivative of displacement is speed, the derivative of speed is acceleration, and the state equation can be deduced easily according to the differential equation of motion control of the structure. In addition, when the observed value is a displacement, since the meanings of the displacement in the state quantity and the displacement in the observed value are the same, the displacement relationship in the observation equation is also easily obtained. In general terms, the displacement and velocity in the state quantity are served by the displacement relationships in the state equation derivation and observation equations, and the displacement in the observation values is served by the displacement calculated for correcting the observation equations. Since the details of this process are common general knowledge, the details of this process are not described in detail in the present invention. It should be noted that the speed in the present invention is equivalent to an intermediate quantity, and no output is required, its existence is only the derivation service of the state equation, and its calculation is completed by iterative algorithm iteration.
According to the type of the observed value, the equation relation for solving the observed value is deduced according to the motion control differential equation of the structure in the step 1 and based on the knowledge of linear algebraic matrix operation, mathematical term shifting, mathematical merging of similar terms and the like;
or,
according to the type of the observed value, carrying out output setting of the corresponding observed value according to the structure finite element model in the step 1, and taking the output setting as an observation equation; the noise effect is considered in the process;
step 4, the vector composed of the initial displacement of the structure, the initial velocity of the structure and the initial value of each elastic modulus is called initial state quantity, and is represented by X 0 Representing and obtaining covariance matrix of initial state quantity according to Kalman filter algorithm principle, namely initial state quantity covariance for short, using symbol P 0 Representation, wherein χ 0 And P 0 State quantity and state quantity covariance, respectively referred to as time step 0 (start step);
step 5, carrying out preliminary identification based on an unscented Kalman filter algorithm, wherein the process is as follows:
step 5.1, based on the UT transformation principle of the unscented kalman filter algorithm, using the state quantity χ of the (k-1) th time step k-1 And state quantity covariance P k-1 Generating (2n+1) sigma points, and solving the state quantity corresponding to each sigma point through a state equationWherein k starts from 1 and k.epsilon.1, N]N is the total time step number, N is the dimension of the state quantity, i is the ith sigma point, and i E [1,2n+1 ]]；
Step 5.2, the time update step based on the unscented Kalman filter algorithm completes the update of the state quantity and the state quantity covariance from the (k-1) th time step to the kth time step, respectively written asAnd->The formula is as follows:
in the method, in the process of the invention,and->Weight values of the ith sigma point of the kth time step, respectively, +.>For the state quantity estimated value corresponding to the ith sigma point of the kth time step, Q k Noise for the kth time step;
step 5.3, using the UT transformation principle based on the unscented kalman filter algorithm, updated in step 5.2Andgenerating (2n+1) sigma points, and solving an observation estimated value corresponding to each sigma point through an observation equation>Step 5.4, calculating and outputting a measurement predicted value of the kth time step based on a measurement update step of the unscented Kalman filter algorithm>And is also provided with
In the method, in the process of the invention,weight value for the ith sigma point of the kth time step,/for the kth time step>The observation estimated value corresponding to the ith sigma point in the kth time step is obtained;
step 5.5, calculating the observed error epsilon of the kth time step based on the measurement updating step of the unscented Kalman filter algorithm k And (2) and
wherein y is k As an observation of the kth time step,measuring a predicted value for the kth time step;
step 5.6, calculating the measurement prediction covariance P of the kth time step based on the measurement update step of the unscented Kalman filter algorithm yy,k And (2) and
in the method, in the process of the invention,weight value for the ith sigma point of the kth time step,/for the kth time step>For the observation estimate corresponding to the kth time step i sigma point,/for the k time step i sigma point>For the measurement prediction value of the kth time step, R k Noise for the kth time step;
step 5.7 epsilon calculated based on step 5.5 and step 5.6 k And P yy,k Construction sensitivity parameter eta k And (2) andand calculate and output eta for each step k A value;
step 5.8, calculating the kth time step based on the measurement update step of the unscented Kalman filter algorithmAnd->Cross covariance P of (2) xy,k ，/>
Step 5.9, updating the Kalman gain matrix of the kth time step:
step 5.10, updating and outputting the state quantity of the kth time step:
step 5.11, updating and outputting the state quantity covariance of the kth time step:
step 5.12, the time step becomes (k+1), repeat step 5.1-step 5.11 until the maximum time step N is completed, i.e. until the cycle is over.
Step 6, drawing a sensitivity parameter time curve output in the step 5.7, and if the whole curve is stable and no impulse response appears (see figure 1), calling an adaptive unscented Kalman filter algorithm is not needed, and the identification is carried out according to a conventional unscented Kalman filter algorithm, namely, the step 5 (but ignores the step 5.5 and the step 5.7); if eta k If peak pulse appears in the time course curve (see figure 2), an adaptive unscented Kalman filter algorithm is required to be called (step 7) to identify damagePosition and make the maximum sensitivity parameter value before peak pulse equal to the sensitivity parameter threshold eta 0 (see FIG. 3, where FIG. 3 is a partial view of FIG. 2).
And 7, identifying based on an adaptive unscented Kalman filter algorithm, wherein the process is as follows:
step 7.1, the same step 5.1;
step 7.2, the synchronization step 5.2;
step 7.3, and step 5.3;
step 7.4, the same step 5.4;
step 7.5, the synchronization step 5.5;
step 7.6, the synchronization step 5.6;
step 7.7, the same step 5.7;
step 7.8, the synchronization step 5.8;
step 7.9, and the step 5.9 is performed;
step 7.10, and step 5.10;
step 7.11, and step 5.11;
step 7.12, judging η calculated in step 7.7 k And sensitivity parameter threshold eta 0 If eta k ＜η 0 The time step is changed into (k+1), and the steps 7.1 to 7.11 are repeated to continue calculation; if eta k ≥η 0 Continuously executing the steps 7.13 to 7.18;
in step 7.13, a vector with an initial value of 0 and a dimension of n is set, denoted by letter L, and it should be noted that the character representing the vector may be selected, and is denoted by letter L.
Step 7.14, covariance the state quantityMarking the row number or column number of the covariance value corresponding to the first elastic modulus parameter in the main diagonal element as m, and adding the state quantity covariance +.>The row or column number of the covariance value corresponding to the last elastic modulus parameter in the main diagonal element is recorded asl, the number of total elastic modulus parameters is (l-m+1).
Taking the calculation of step 7.11All major diagonal elements of (a) constitute a new diagonal matrix ++>And the position of the original diagonal element is kept unchanged. Sequentially enlarge->The corresponding covariance value of each elastic modulus parameter of the rubber belt is thatAnd only one covariance value is enlarged at a time,/->The remaining element values of (2) remain unchanged, wherein +.>And->Representing the covariance values at z-position for each row and column, respectively, as a scalar, where λ=1×10 ω And 10 ω Equal to the initial state quantity covariance P 0 Reciprocal of the smallest order of magnitude in (a); the initial value of z is m, and z is ∈ [ m, l-m+1 ]]. Calculated according to z=m +.>And +.7.10 calculated>Executing one-step complete unscented Kalman filtering operation, namely executing the steps 7.1 to 7.11, and outputting eta k Let L (z) =η k 。
Step 7.15, let z=m+1, continue to execute step 7.14 until z=l-m+1 ends.
Step 7.16, not counting zero value, finding the position number corresponding to the minimum value in L, and marking as z min Z, i.e. z min Is the location of the injury.
Step 7.17, only makeElement->Expansion by 20 times, wherein->The number of rows and columns are represented as the covariance value at the z position, and the multiple 20 is derived from the numerical simulation statistics.
Step 7.18, the time step becomes (k+1), repeat step 7.1-step 7.17 until the maximum time step N is completed, namely until the cycle is finished, find all damage positions and output.
Examples
For a full description of the invention, the invention is illustrated in embodiments with a vehicle-to-bridge coupling system.
To fully illustrate the present invention, the present embodiment will first be described with reference to the vehicle-to-bridge coupling system shown in fig. 4:
the vehicle-bridge coupling system comprises a vehicle body mass 1 of a quarter vehicle model, a suspension rigidity 2 between the vehicle body and tires of the quarter vehicle model, a suspension damping 3 between the vehicle body and tires of the quarter vehicle model, a tire mass 4 of the quarter vehicle model, a contact rigidity 5 between the tires and a bridge of the quarter vehicle model, a tire-bridge contact point 6, a fixed end 7 of a simple support boundary constraint, a beam unit 8, a beam unit node 9 and a sliding end 10 of the simple support boundary constraint;
the contact point 6 between the tire and the bridge means that the tire is always closely connected with the bridge in the running process of the vehicle, and the tire and the bridge are not separated;
the beam units 8 are not limited to the positions shown in the drawings, and 6 beam units are all shown in the drawings;
the beam unit nodes 9 are not limited to the positions shown in the figure, and the rest of the beam unit nodes with the same shape symbols comprise beam unit nodes at two ends of the bridge.
The implementation process of the method is as follows:
1. based on the interaction theory of the vehicle and the structural power and by combining the finite element theory, a motion control differential equation of the vehicle-bridge coupling system is deduced, and a contact force relationship, namely an interaction force equation between the tire and the bridge deck, is deduced based on the motion control differential equation of the vehicle part, so that external load excitation applied to the bridge can be calculated when the vehicle passes through the bridge.
2. Based on finite element theory, the displacement and speed states of the bridge structure can be represented by the displacement and speed of the degree of freedom of the nodes of each beam unit, before dynamic load action, the displacement and speed of the degree of freedom of each node are considered to be 0, and the initial value of the elastic modulus of each beam unit can be obtained based on the material composition of the bridge structure, so that the initial state quantity χ is calculated 0 Based on Kalman filter principle, initial state quantity covariance P is obtained 0 。
3. In the load action process, the vertical displacement of each beam unit node of the bridge can be acquired or calculated by a sensor or a numerical simulation means, so that the observation value is known.
4. And (3) identifying the damage position of the bridge structure based on the steps 1-7 and the initial information.
For the convenience of the application description of the present invention, the key parts of the algorithm are further explained herein, and the initial state quantity χ is selected respectively 0 Further described with respect to the intermediate vector L, the initial state quantity is selected with emphasis on the covariance P of the initial state quantity 0 The setting of the intermediate vector L, and the last identified state quantity are closely related. According to the foregoing, the present embodiment builds a bridge finite element model based on Euler-Bernoulli beam units, and since each beam unit has 2 nodes, each node has 2 degrees of freedom, while according to FIG. 4, the present embodiment has a total of 6 beam units, so that there are 7 nodes, including 14 self-membersDegree of freedom. Therefore, the displacement and velocity states of the bridge are respectively represented by 14 parameters, and 6 elastic modulus parameters are considered, so the state quantity dimension of the embodiment is (14+14+6=34). According to the method introduction, the dimensions of L are likewise equal to 34 and their initial values are all 0. Similarly, for the convenience of expressing the recognition effect, it is assumed that the elastic modulus parameters at the 30 th and 31 st positions are damaged by reduction, and the elastic moduli at the 30 th and 31 st positions in the state quantity respectively correspond to the two beam units of the bridge, and specific numbers can be defined in advance. By means of calculation, abnormal state quantity parameters at two positions 30 and 31 can be preferentially identified, and then the damage position can be rapidly determined through the beam unit number.
The second embodiment is as follows:
the present embodiment is a storage medium having at least one instruction stored therein, the at least one instruction loaded and executed by a processor to implement a method for non-destructive identification of a damaged bridge location.
It should be understood that the storage media described in this embodiment include, but are not limited to, magnetic storage media and optical storage media; the magnetic storage medium includes, but is not limited to, RAM, ROM, and other hard disk, U-disk, etc. storage media.
And a third specific embodiment:
the embodiment is a nondestructive identification device for a damaged position of a bridge, the device comprises a processor and a memory, wherein at least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to realize a nondestructive identification method for the damaged position of the bridge.
It should be understood that the device described in this embodiment includes, but is not limited to, a device including a processor and a memory, and may further include other devices corresponding to units or modules having information collecting, information interaction, and control functions, for example, the device may further include a signal collecting device, etc. Including but not limited to PCs, workstations, mobile devices, etc.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (10)

1. A nondestructive identification method for a damaged position of a bridge comprises the following steps:
for the bridge structure, determining initial values of corresponding states of the bridge structure, and forming initial state quantity χ 0 And determining covariance matrix of initial state quantity according to Kalman filtering principle, namely initial state quantity covariance P 0 The method comprises the steps of carrying out a first treatment on the surface of the Wherein χ is 0 And P 0 State quantity and state quantity covariance, respectively, referred to as time step 0;
preliminary identification is carried out based on an unscented Kalman filter algorithm, and in the process of preliminary identification based on the unscented Kalman filter algorithm, the observation error epsilon of the kth time step needs to be calculated based on a measurement updating step of the unscented Kalman filter algorithm k And a k-th time step of metrology prediction covariance P yy,k And based on epsilon k And P yy,k Calculating and outputting the corresponding sensitive parameters of each step
Then the output sensitivity parameter eta is plotted k If eta k The time-course curve has peak pulse, then based on the self-adaptive unscented Kalman filter algorithm, the damage position is identified, which is characterized in that:
in the process of identification based on the adaptive unscented Kalman filter algorithm, the calculated eta is required to be judged k And sensitivity parameter threshold eta 0 If eta k ＜η 0 Continuing to identify based on the unscented Kalman filter algorithm; if eta k ≥η 0 The following steps are continued:
setting an initial value to 0 and dimension to be equal to initial state quantity χ 0 Is denoted by the letter L; taking state quantity covarianceAll major diagonal elements of (a) constitute a new diagonal matrix ++>The positions of the original diagonal elements are kept unchanged; sequentially enlargeThe corresponding covariance value of each elastic modulus parameter is expanded each time, one-step complete unscented Kalman filtering operation is carried out, and aiming at the expansion of the row number or the column number z corresponding to the covariance value, one-step complete unscented Kalman filtering operation is carried out to obtain a sensitivity parameter eta k Let L (z) =η k The method comprises the steps of carrying out a first treatment on the surface of the Find the minimum L-corresponding position number z min This location is the lesion location; then let->Expanding 20 times, and continuing to execute the (k+1) th time step, and judging eta again k+1 And sensitivity parameter threshold eta 0 Until all cycles are completed to obtain all lesion locations.
2. The method for non-destructive identification of a damaged bridge location according to claim 1, wherein: and selecting the vertical displacement response of each beam unit node as an observation value y in the process of identifying by using the unscented Kalman filter algorithm and in the process of identifying by using the adaptive unscented Kalman filter algorithm.
3. The method for non-destructive identification of a damaged bridge location according to claim 2, wherein: the bridge structure corresponding state comprises the elastic modulus of each bridge beam unit, and the displacement and the speed of the bridge structure.
4. A method for the non-destructive identification of a damaged site of a bridge according to claim 1,2 or 3, characterized in that: in the process of identification based on the adaptive unscented Kalman filter algorithm, the sensitivity parameter eta is calculated k The process of (1) comprises the following steps:
step 7.1, based on the UT transformation principle of the unscented kalman filter algorithm, using the state quantity χ of the (k-1) th time step k-1 And state quantity covariance P k-1 Generating (2n+1) sigma points, and solving the state quantity corresponding to each sigma point through a state equationWherein k starts from 1 and k.epsilon.1, N]N is the total time step number, N is the dimension of the state quantity, i is the ith sigma point, and i E [1,2n+1 ]]；
Step 7.2, the time update step based on the unscented Kalman filter algorithm completes the update of the state quantity and the state quantity covariance from the (k-1) th time step to the kth time step, respectively written asAnd->The formula is as follows:
in the method, in the process of the invention,and->Weight values of the ith sigma point of the kth time step, respectively, +.>For the state quantity estimated value corresponding to the ith sigma point of the kth time step, Q k Noise for the kth time step;
step 7.3, using the UT transformation principle based on the unscented kalman filter algorithm, updated in step 7.2And->Generating (2n+1) sigma points, and solving an observation estimated value corresponding to each sigma point through an observation equation>
Step 7.4, calculating and outputting the measurement predicted value of the kth time step based on the measurement update step of the unscented Kalman filter algorithmAnd->
In the method, in the process of the invention,weight value for the ith sigma point of the kth time step,/for the kth time step>The observation estimated value corresponding to the ith sigma point in the kth time step is obtained;
step 7.5, based on the unscented cardMeasurement update step of the Kalman filter algorithm calculates the observed error ε of the kth time step k And (2) and
wherein y is k As an observation of the kth time step,measuring a predicted value for the kth time step;
step 7.6, calculating the measurement prediction covariance P of the kth time step based on the measurement update step of the unscented Kalman filter algorithm yy,k And (2) and
in the method, in the process of the invention,weight value for the ith sigma point of the kth time step,/for the kth time step>For the observation estimate corresponding to the kth time step i sigma point,/for the k time step i sigma point>For the measurement prediction value of the kth time step, R k Noise for the kth time step;
step 7.7 epsilon calculated based on step 7.5 and step 7.6 k And P yy,k Construction sensitivity parameter eta k And (2) andand calculate and output eta for each step k Values.
5. The method for non-destructive identification of a damaged bridge location according to claim 4, wherein: based on adaptive unscented Kalman filterIn the process of identifying the wave device algorithm, the calculation sensitivity parameter eta is obtained k Then calculate the kth time stepAnd->Cross covariance P of (2) xy,k And updating data, wherein the specific process comprises the following steps:
step 7.8, calculating the kth time step based on the measurement update step of the unscented Kalman filter algorithmAnd->Cross covariance P of (2) xy,k ，/>
Step 7.9, updating the Kalman gain matrix of the kth time step:
step 7.10, updating and outputting the state quantity of the kth time step:
step 7.11, updating and outputting the state quantity covariance of the kth time step:
6. the method for non-destructive identification of a damaged bridge location according to claim 5, wherein: find the minimum L-corresponding position number z min Specific (1)The process comprises the following steps:
step 7.14, covariance the state quantity of the kth time stepMarking the row number or column number of the covariance value corresponding to the first elastic modulus parameter in the main diagonal element as m, and adding the state quantity covariance +.>The row number or column number of the covariance value corresponding to the last elastic modulus parameter in the main diagonal element is marked as l, and the total number of the elastic modulus parameters is (l-m+1);
taking the current time stepAll major diagonal elements of (a) constitute a new diagonal matrix ++>The positions of the original diagonal elements are kept unchanged; sequentially enlarge->The corresponding covariance value of each elastic modulus parameter of the rubber belt is thatAnd only one covariance value is enlarged at a time,/->The remaining element values of (2) remain unchanged, wherein +.>And->Respectively represent the number of rows and columnsThe values are the covariance values at the z position, which are a scalar; lambda is an expansion multiple;
the initial value of z is m, and z is ∈ [ m, l-m+1 ]]The method comprises the steps of carrying out a first treatment on the surface of the Calculated from z=mAnd the state quantity of the kth time step +.>Executing one-step complete unscented Kalman filtering operation, namely executing the steps 7.1 to 7.11, and outputting eta k Let L (z) =η k ；
Step 7.15, let z=m+1, continue to execute step 7.14 until z=l-m+1 ends;
step 7.16, not counting zero value, finding the position number corresponding to the minimum value in L, and marking as z min Z, i.e. z min Is the location of the injury.
7. The method for non-destructive identification of a damaged bridge location according to claim 6, wherein: the expansion factor λ=1×10 ω ，10 ω Equal to the initial state quantity covariance P 0 Reciprocal of the smallest order of magnitude in (c).
8. The method for non-destructive identification of a damaged bridge location according to claim 7, wherein: the motion control differential equation or the finite element model corresponding to the bridge structure is built based on Euler-Bernoulli beam units.
9. A storage medium, characterized by: the storage medium having stored therein at least one instruction that is loaded and executed by a processor to implement a method of non-destructive identification of a bridge damage location according to any one of claims 1 to 8.
10. The nondestructive identification equipment for the damaged position of the bridge is characterized by comprising the following components: the apparatus comprising a processor and a memory having stored therein at least one instruction that is loaded and executed by the processor to implement a method of non-destructive identification of a bridge damage location according to any one of claims 1 to 8.
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